Answer:
a) z-score = 4
b) z-score = 2
c) z-score = 1
Step-by-step explanation:
* Lets revise some definition to solve the problem
- The mean of the distribution of sample means is called M
- The standard deviation of the distribution of sample means is
called σM (standard error)
- σM = σ/√n , where σ is the standard deviation and n is the sample size
- z-score = (M - μ)/σM, where μ is the mean of the population
* Lets solve the problem
∵ The sample size n = 25
∵ The sample mean M = 68
a)
∵ The mean of population μ = 60
∵ The standard deviation σ = 10
- Lets find σM to find z-score
∵ σM = σ/√n
∴ σM = 10/√25 = 10/5 = 2
- Lets find z-score
∵ z-score = (M - μ)/σM
∴ z-score = (68 - 60)/2 = 8/2 = 4
* z-score = 4
b)
∵ The mean of population μ = 60
∵ The standard deviation σ = 20
- Lets find σM to find z-score
∵ σM = σ/√n
∴ σM = 20/√25 = 20/5 = 4
- Lets find z-score
∵ z-score = (M - μ)/σM
∴ z-score = (68 - 60)/4 = 8/4 = 2
* z-score = 2
c)
∵ The mean of population μ = 60
∵ The standard deviation σ = 40
- Lets find σM to find z-score
∵ σM = σ/√n
∴ σM = 40/√25 = 40/5 = 8
- Lets find z-score
∵ z-score = (M - μ)/σM
∴ z-score = (68 - 60)/8 = 8/8 = 1
* z-score = 1
