Question

A sample of n = 16 scores is selected from a normal population with μ = 60 and σ= 20.a. What is the probability that the sample mean will be greater than 50?Proportion=b. What is the probability that the sample mean will be less than 56?Proportion=c. What sample mean scores form the boundaries for the middle 80 %?Proportion=

Answer 1

Step-by-step explanation

In this problem, we have a sample with n = 16, and the population has:

• mean value μ = 60,

• standard deviation σ = 20.

(a) We want to know the probability that the sample mean will be greater than 50. To compute this probability, we compute the z-score for x = 50:

`z=(x-\mu)/(\sigma)=(50-60)/(20)=-0.5.`

Using a table probability for the z-scores, we get:

`P(X>50)=P(Z>-0.5)=0.6915.`

(b) We want to know the probability that the sample mean will be less than 50. To compute this probability, we compute the z-score for x = 56:

`z=(x-\mu)/(\sigma)=(56-60)/(20)=-0.2.`

Using a table probability for the z-scores, we get:

`P(X<56)=P(Z<-0.2)=0.4207.`

(c) To determine the boundaries for the middle 80%, first, we find the z-scores values with a z-score table, we get:

Using these values, we compute the values of the boundaries:

Answer

(a) Proportion = 0.6915

(b) Proportion = 0.4207

(c) Boundaries: x₁ = 34.364 and x₂ = 85.636