Given a standardized normal distribution (with a mean of 0 and a standard deviat

ID: 3330532 • Letter: G

Question

Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1), complete parts (a) through (c) below.

a. What is the probability that Z is between -1.52 and 1.87?

The probability that Z is between -1.52 and 1.87is ????

(Round to four decimal places as needed.)

b. What is the value of Z if only6.5% of all possible Z values are larger?

The value of Z if only 6.5% of all possible Z values are larger is ???

(Round to two decimal places as needed.)

c. Between what two values of Z (symmetrically distributed around the mean) will 72.86% of all possible Z values be contained?

The two values of Z for which 72.86% of all possible Z values are contained between are ????and ?????

(Use ascending order. Round to two decimal places as needed.)

Answers to Questions asked:
(a) 0.9050

(b) 1.51

(a) P(-1.52 < Z < 1.87):

Case 1:

For x from - 1.52 to mid value:

Since Z is negative, it lies on LHS of midvale.

Table of Area Under Standard Normal Curve gives area from mid value to Z = - 1.52 on LHS of midvalue as area = 0.4357.

Case 2:

For Z from mid value to 1.87.

Table gives area = 0.4693.

So,

P(-1.52 < X< 1.87) = 0.9050

(b) 6.5% of all values larger corresponds to area = 0.5 - 0.065 = 0.435 from mid value to Z.

Table gives Z score corresponding to area = 0.435 as Z = 1.51

So, answer is:

Z = 1.51

Table gives Z score corresponding to area = 0.3643 as Z = 1.10

So, Between Z = - 1.10 and and Z = + 1.10, 72.86% of all possible Z values are contained.

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