Question

Scores on a memory test are normally distributed with a mean of 16 and standard deviation of 10.70.

1) What proportion of people have scores of 18 or higher? 2) Suppose that you randomly select one person from this population. What is the probability that this person will have a score less than 13?

1.

a).6141

b).3859

c).4286

d).5714

2.

a).28

b).72

c).6103

d).3897

Answer 1

The Scores on a memory test are normally distributed with a mean of M = 16 and a standard deviation of S = 10.70. So, for a normal distribution, the probability is calculated by finding the Z score.

a) So, the proportion of people have scores of X = 18 or higher P(X>=8) is calculated by finding the Z score which is calculated as:

So, P(X> =18) =P(Z>0.19) is computed using excel formula for normal distribution which is =1-NORM.S.DIST(0.19,TRUE) thus it results in P(X>=18) = 0.4246

So, c).4286

b) For the probability that this person will have a score of less than 13, P(X<13) is calculated using Z -a score which is calculated as:

So, P(X<13) = P(Z<-0.28) is calculated using excel formula for normal distribution which is =NORM.S.DIST(-0.28,TRUE),

Thus P(X<13) computed as 0.3897

so, d).3897