Question

1. Suppose that scores on a knowledge test are normally distributed with a mean of 71 and a standard deviation

of 6.

a. Label the curve: Show the mean and the value at each standard deviation:

b. If Angelica scored a 76 on the test, what is her z-score? (Draw her score on the curve above and label)

c. What percent of students did Angelica score higher than?

How can you tell?

d. If 185 students took the test, how many students scored higher than Angelica?

Answer 1

Explanation:

X represent the random variable scores of knowledge test and is given as follows;

X-N (m= 71, s= 6)

A. For this question we can see the distribution in the file attached has a bell shaped graph and symmetrical around 71

B. To calculate the z score, we use the following method

z = (X-m)÷s

z = (76-71)÷6

z= 0.833

C. The probability of P( X> 76) using the standard normal distribution table is P(Z> 0.833) = 1 - P(Z<0.833) = 0.202

D. The number of students that scored more than Angelica is calculated as follows

n = 185×0.202

n= 154.16

154 to 155 students scored higher than Angelica.