# Expert Answer - A polling company reported

Several psychology students are unprepared for a surprise true/false test with 88 questions, and all of their answers are guesses.
a. Find the mean and standard deviation for the number of correct answers for such students.
b. Would it be unusual for a student to pass by guessing (which requires getting at least 66 correct answers)? Why or why not?

Listed below are the durations (in hours) of a simple random sample of all flights of a space shuttle program. Find the range, variance, and standard deviation for the sample data. Is the lowest duration time unusual? Why or why not?
the actual numbers are: 79
94
240
195
165
267
192
376
259
236
381
330
221
242
0

A particular group of men have heights with a mean of 169 cm and a standard deviation of 6 cm. JohnJohn had a height of 173 cm.
a.
What is the positive difference between JohnJohn's height and the mean?
b.
How many standard deviations is that [the difference found in part (a)]?
c.
Convert JohnJohn's height to a z score.
d.
If we consider "usual" heights to be those that convert to z scores between minus−2 and 2, is JohnJohn's height usual or unusual?

In a recent year the magnitudes (Richter scale) of 10,594 earthquakes were recorded. The mean is 1.273 and the standard deviation is 0.551. Consider the magnitudes that are unusual. What are the magnitudes that separate the unusual magnitudes from those that are usual? (Consider a value to be unusual if its z score is less than minus−2 or greater than 2.)

The population of current statistics students has ages with mean muμ and standard deviation sigmaσ. Samples of statistics students are randomly selected so that there are exactly 52 students in each sample. For each sample, the mean age is computed. What does the central limit theorem tell us about the distribution of those mean ages?

Assume that women's heights are normally distributed with a mean given by 62.4, and a standard deviation given by 2.3 σ=2.3 in.
(a) If 1 woman is randomly selected, find the probability that her height is less than 63 in.
(b) If 47 women are randomly selected, find the probability that they have a mean height less than 63 in.

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 49.0 and 59.0 minutes. Find the probability that a given class period runs between 51.5 and 51.75 minutes.

Ted is not particularly creative. He uses the pickup line "If I could rearrange the alphabet, I'd put U and I together." The random variable x is the number of girls Ted approaches before encountering one who reacts positively. Determine whether the table describes a probability distribution. If it does, find its mean and standard deviation.
x P(x)
1 0.001
2 0.028
3 0.103
4 0.286
5 0.339

A polling company reported that 53% of 1018 surveyed adults said that pesticides arepesticides are "very harmful.""very harmful." Complete parts (a) through (d) below.
a. What is the exact value that is 53% of 1018?
b. Could the result from part (a) be the actual number of adults who said that pesticides are pesticides are "very harmful" ?Why or why not?
c. What could be the actual number of adults who said that pesticides are "very harmful"?
d. Among the 1018 respondents, 377 said that pesticides are "not at all harmful." What percentage of respondents said that pesticides are "not at all harmful"?

Listed below are the annual tuition amounts of the 10 most expensive colleges in a country for a recent year. What does this "Top 10" list tell us about the population of all of that country's college tuitions?
\$54455
\$53598
\$54394
\$53940
\$54278
\$53425
\$54394
\$52856
\$54397
\$52994

Find the mean, midrange, median, and mode of the data set.
The mean of the data set is
\$.
(Round to two decimal places as needed.)
The midrange of the data set is
\$.
(Round to two decimal places as needed.)
The median of the data set is
\$.
(Round to two decimal places as needed.)
What is (are) the mode(s) of the data set?
Select the correct choice below and, if necessary, fill in the answer box within your choice.
A.
The mode(s) of the data set is (are)
\$.
(use a comma to separate answers as needed. Round to two decimal places as needed.)
B.
There is no mode.
What does this "Top 10" list tell us about the population of all the country's college tuitions?
A.
All colleges have tuitions around the midrange.
B.
All colleges have tuitions around the mode.
C.
All colleges have tuitions around the median.
D.
All colleges have tuitions around the mean.
E.
Nothing meaningful can be concluded from this information except that these are the largest tuitions of colleges in the country for a recent year.

The probability of flu symptoms for a person not receiving any treatment is 0.032.
In a clinical trial of a common drug used to lower cholesterol, 34 of 983 people treated experienced flu symptoms. Assuming the drug has no effect on the likelihood of flu symptoms, estimate the probability that at least 34 people experience flu symptoms. What do these results suggest about flu symptoms as an adverse reaction to the drug?
(a)
P(X ≥34)equals=
(Round to four decimal places as needed.)(b) What does the result from part (a) suggest?
A.
The drug has no effect on flu symptoms because
x≥34
is highly unlikely.
B.
The drug has no effect on flu symptoms because
x ≥34
is not highly unlikely.
C.
The drug increases the likelihood of flu symptoms because
x≥34
is highly unlikely.
D.
The drug increases the likelihood of flu symptoms because
x≥34
is not highly unlikely
-----------
A tire company produced a batch of
5,300
tires that includes exactly
210
that are defective.
a. If 4 tires are randomly selected for installation on a car, what is the probability that they are all good?
b. If 100 tires are randomly selected for shipment to an outlet, what is the probability that they are all good? Should this outlet plan to deal with defective tires returned byconsumers?
a. If 4 tires are randomly selected for installation on a car, what is the probability that they are all good?(Round to three decimal places as needed.)
b. If 100 tires are randomly selected for shipment to an outlet what is the probability that they are all good?
(Round to three decimal places as needed.)Should this outlet plan to deal with defective tires returned by consumers?
A.
Yes, because there is a very large chance that all 100 tires are good.
B.
Yes, because there is a very small chance that all 100 tires are good.
C.
No, because there is a very large chance that all 100 tires are good.
D.
No, because there is a very small chance that all 100 tires are good.

Find the indicated area under the curve of the standard normal distribution, then convert it to a percentage and fill in the blank.
About _____% of the area is between
z= −1.8
and
z=1.8
(or within 1.8 standard deviations of the mean).
Click to view page 1 of the table.
___% of the area is between z= −1.8 and z=1.8 (or within 1.8 standard deviations of the mean).Negative z Scores Standard Normal (z) Distribution: Cumulative Area from the Left z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 negative 3.50 and lower .0001
-3.4 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0002
-3.3 .0005 .0005 .0005 .0004 .0004 .0004 .0004 .0004 .0004 .0003
-3.2 .0007 .0007 .0006 .0006 .0006 .0006 .0006 .0005 .0005 .0005
-3.1 .0010 .0009 .0009 .0009 .0008 .0008 .0008 .0008 .0007 .0007
-3.0 .0013 .0013 .0013 .0012 .0012 .0011 .0011 .0011 .0010 .0010
-2.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014
-2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 .0019
-2.7 .0035 .0034 .0033 .0032 .0031 .0030 .0029 .0028 .0027 .0026
-2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0039 .0038 .0037 .0036
-2.5 .0062 .0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 .0048
-2.4 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 .0064
-2.3 .0107 .0104 .0102 .0099 .0096 .0094 .0091 .0089 .0087 .0084
-2.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110
-2.1 .0179 .0174 .0170 .0166 .0162 .0158 .0154 .0150 .0146 .0143
-2.0 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .0192 .0188 .0183
-1.9 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0239 .0233
-1.8 .0359 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0294
-1.7 .0446 .0436 .0427 .0418 .0409 .0401 .0392 .0384 .0375 .0367
-1.6 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455
-1.5 .0668 .0655 .0643 .0630 .0618 .0606 .0594 .0582 .0571 .0559
-1.4 .0808 .0793 .0778 .0764 .0749 .0735 .0721 .0708 .0694 .0681
-1.3 .0968 .0951 .0934 .0918 .0901 .0885 .0869 .0853 .0838 .0823
-1.2 .1151 .1131 .1112 .1093 .1075 .1056 .1038 .1020 .1003 .0985
-1.1 .1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170
-1.0 .1587 .1562 .1539 .1515 .1492 .1469 .1446 .1423 .1401 .1379
-0.9 .1841 .1814 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611
-0.8 .2119 .2090 .2061 .2033 .2005 .1977 .1949 .1922 .1894 .1867
-0.7 .2420 .2389 .2358 .2327 .2296 .2266 .2236 .2206 .2177 .2148
-0.6 .2743 .2709 .2676 .2643 .2611 .2578 .2546 .2514 .2483 .2451
-0.5 .3085 .3050 .3015 .2981 .2946 .2912 .2877 .2843 .2810 .2776
-0.4 .3446 .3409 .3372 .3336 .3300 .3264 .3228 .3192 .3156 .3121
-0.3 .3821 .3783 .3745 .3707 .3669 .3632 .3594 .3557 .3520 .3483
-0.2 .4207 .4168 .4129 .4090 .4052 .4013 .3974 .3936 .3897 .3859
-0.1 .4602 .4562 .4522 .4483 .4443 .4404 .4364 .4325 .4286 .4247
-0.0 .5000 .4960 .4920 .4880 .4840 .4801 .4761 .4721 .4681 .4641
Note: For values of z below -3.49, use 0.0001 for the area.
* use these common values that result from interpolation:
z score Area
-1.645 0.0500
-2.575 0.0050Positive z Scores
Standard Normal (z) Distribution: Cumulative Area from the Left
z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09
0.0 .5000 .5040 .5080 .5120 .5160 .5199 .5239 .5279 .5319 .5359
0.1 .5398 .5438 .5478 .5517 .5557 .5596 .5636 .5675 .5714 .5753
0.2 .5793 .5832 .5871 .5910 .5948 .5987 .6026 .6064 .6103 .6141
0.3 .6179 .6217 .6255 .6293 .6331 .6368 .6406 .6443 .6480 .6517
0.4 .6554 .6591 .6628 .6664 .6700 .6736 .6772 .6808 .6844 .6879
0.5 .6915 .6950 .6985 .7019 .7054 .7088 .7123 .7157 .7190 .7224
0.6 .7257 .7291 .7324 .7357 .7389 .7422 .7454 .7486 .7517 .7549
0.7 .7580 .7611 .7642 .7673 .7704 .7734 .7764 .7794 .7823 .7852
0.8 .7881 .7910 .7939 .7967 .7995 .8023 .8051 .8078 .8106 .8133
0.9 .8159 .8186 .8212 .8238 .8264 .8289 .8315 .8340 .8365 .8389
1.0 .8413 .8438 .8461 .8485 .8508 .8531 .8554 .8577 .8599 .8621
1.1 .8643 .8665 .8686 .8708 .8729 .8749 .8770 .8790 .8810 .8830
1.2 .8849 .8869 .8888 .8907 .8925 .8944 .8962 .8980 .8997 .9015
1.3 .9032 .9049 .9066 .9082 .9099 .9115 .9131 .9147 .9162 .9177
1.4 .9192 .9207 .9222 .9236 .9251 .9265 .9279 .9292 .9306 .9319
1.5 .9332 .9345 .9357 .9370 .9382 .9394 .9406 .9418 .9429 .9441
1.6 .9452 .9463 .9474 .9484 .9495 .9505 .9515 .9525 .9535 .9545
1.7 .9554 .9564 .9573 .9582 .9591 .9599 .9608 .9616 .9625 .9633
1.8 .9641 .9649 .9656 .9664 .9671 .9678 .9686 .9693 .9699 .9706
1.9 .9713 .9719 .9726 .9732 .9738 .9744 .9750 .9756 .9761 .9767
2.0 .9772 .9778 .9783 .9788 .9793 .9798 .9803 .9808 .9812 .9817
2.1 .9821 .9826 .9830 .9834 .9838 .9842 .9846 .9850 .9854 .9857
2.2 .9861 .9864 .9868 .9871 .9875 .9878 .9881 .9884 .9887 .9890
2.3 .9893 .9896 .9898 .9901 .9904 .9906 .9909 .9911 .9913 .9916
2.4 .9918 .9920 .9922 .9925 .9927 .9929 .9931 .9932 .9934 .9936
2.5 .9938 .9940 .9941 .9943 .9945 .9946 .9948 .9949 .9951 .9952
2.6 .9953 .99

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial.
n=99,
x=55,
p=0.65

Suppose that we want to estimate the mean PCB (Polychlorinated biphenyl) level in white croaker fish from the San Francisco Bay. The sample we select has a mean of parts per million and a standard deviation of parts per million. For each of the following sampling scenarios, determine which test statistic is appropriate to use when making inference statements about the population mean.(In the table, refers to a variable having a standard normal distribution, and refers to a variable having a t distribution.) Sampling Scenario Zt could use either Z or tunclear(1) The sample has size 13, and it is from a population with a distribution about which we know very little. (2) The sample has size 20, and it is from a normally distributed population with unknown standard deviation. (3) The sample has size 105, and it is from a non-normally distributed population. (4) The sample has size 10, and it is from a normally distributed population with a known standard deviation of 54. (5) The sample has size 90, and it is from a non-normally distributed population with a known standard deviation of 54.

Richard has just been given a 4-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended class recently, he doesn't know any of the answers. Assuming that Richard guesses on all four questions, find the indicated probabilities. (Round your answers to three decimal places.)
(a) What is the probability that he will answer all questions correctly?