A set of final examination grades in an introductory statistics course is normal

ID: 3050237 • Letter: A

Question

A set of final examination grades in an introductory statistics course is normally distributed, with a mean of

7676

and a standard deviation of

77.

Complete parts (a) through (d).

What is the probability that a student scored below

8585

on this exam?The probability that a student scored below

8585

0.90150.9015.

(Round to four decimal places as needed.)

What is the probability that a student scored between

6969

and

9292?

The probability that a student scored between

6969

and

9292

0.83030.8303.

(Round to four decimal places as needed.)

The probability is

55%

that a student taking the test scores higher than what grade?The probability is

55%

that a student taking the test scores higher than

nothing.

(Round to the nearest integer as needed.)

Solution:- Given that mean = 76 ,sd = 7

a. The probability that a student scored below 85 is 0.9015
P(X < 85) = P(Z < (85-76)/7)
= P(Z < 1.2857)
= 0.9015

b. The probability that a student scored between 69 and 92 is 0.8303
=> P(69 < X < 92) = P((69-76)/7 < Z < (92-76)/7)
= P(-1 < Z < 2.2857)
= 0.8303

c. The probability is 55% that a student taking the test scores higher than is 77
x = zs+u = 0.1257*7+76 = 76.8799 = 77

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