# QNT 275 Week 4 Practice Set

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QNT 275 Week 4 Practice Set

Chapter 06, Section 6.1, Problem 013

Correct.

Find the area under the standard normal curve between z=-1.53 and z=2.37.

A=

the tolerance is +/-2%

Chapter 06, Section 6.1, Problem 015a

Correct.

Obtain the area under the standard normal curve to the right of z=1.37.

A=

the tolerance is +/-2%

Chapter 06, Section 6.2, Problem 019a

Correct.

Find the z value for x=33 for a normal distribution with μ=30 and σ=5.

z=

exact number, no tolerance

Chapter 06, Section 6.2, Intelligent Tutoring Problem 023

Compute probabilities.

Recall the following definitions from section 6.4 of the text.

The area under the normal curve from x = a to x = b with given mean and standard deviation is the probability that x assumes a value between x = a and x = b. If we are using Table IV in Appendix C, we need to standardize the random variable x using the formula z = (x− µ)/σ, before using the table.

Alternatively, you may use a graphing calculator to obtain more accurate calculations without standardizing the random variable x.

For example, using a TI83 plus we calculate the area under the normal curve from x = a to x = b by using the

normalcdf(a,b,µ,σ)

where µ is the mean and σ is the standard deviation of the normal distribution. We use 1E99 for ∞ and −1E99 for −∞, if needed.

Chapter 06, Section 6.2, Intelligent Tutoring Problem 023

Let x be a continuous random variable that is normally distributed with a mean of 24 and a standard deviation of 5.

(a) Standardize the variable value x = 26.9.

z =

(b) Standardize the variable value x = 49.0.

z =

Attempts: 1 of 3 used

Chapter 06, Section 6.2, Intelligent Tutoring Problem 023

Let x be a continuous random variable that is normally distributed with a mean of 24 and a standard deviation of 5.

(a) Write a cumulative probability statement for the area under the normal curve to find the probability that x assumes a value between 26.9 and 49.0:

(b) Write an equivalent standardized probability statement for (a) above using the results obtained in the previous step:

Attempts: 1 of 3 used

Chapter 06, Section 6.2, Intelligent Tutoring Problem 023

Area under normal curve between x = 26.9 and x = 49.0 is given by

P(26.9 < x < 49.0) = P( 0.58 < z < 5) =

the tolerance is +/-2%

Attempts: 1 of 3 used

Chapter 06, Section 6.2, Intelligent Tutoring Problem 023

Now, if the mean is 26 and the standard deviation is 6, find the probability that x assumes a value between 29.5 and 56.0.

The probability =

the tolerance is +/-2%

Chapter 07, Section 7.1, Video Quiz 1

Please view the following video before answering this question. Distribution of the Sample Mean

The 5 ages of the population have one mean. However, when looking at the 10 samples of 3 of those means, there are 10 means – one for each sample. State the symbols for the one mean and then the 10 means.

µ,  x¯.

x¯,  x¯.

x¯, µ.

µ, µ.