Question

Use the table for the Standard Normal table to obtain the following probabilities

(while also reflecting full clarity and proper notation)

:

Pr (Z < 1.45) =?

Pr (-1 < Z < 1) =?

Find a value Z

c

such that Pr (Z < Z

c

) = .8790

Find a value Z

c

such that Pr (-Z

c

< Z < Z

c

) = .8384

2.

If X is normal random variable with mean 100 and standard deviation of 15, that is

X ~ N (100, 15), determine the Pr (90 < X < 110)?

3. Suppose the time required to complete a college achievement test was found to be normally

distributed, with a mean time of 90 minutes and a standard deviation of 15 minutes. For the

problems below, present a solution using clear notation conveying how these problems are related

to an appropriate restatement employing the standard normal distribution.

(Part a) What proportions of the students are expected to finish within a 2 hr (120 minute) time

allotment? Note that this problem is equivalent to asking what is the probability of a student

finishing within two hours?

(Part b) What time allotment should be chosen to allow just enough time for 90% of the students

to complete the test? Explain your solution clearly.

________________________________________________________________________

Partial Answers:

.9265 , .6826 , 1.17 , 1.40 , .4908 , .9772 , 109.2

Answer 1