  We have a normally distributed population of scores with μ = 25 and σ = 5. We have drawn a large number of random samples with a particular sample size of n = 10 from this population.We want to know what the probability that a sample mean will be equal to or greater than 23.First, what is the z-score for our sample mean of interest, 23?

Question

We have a normally distributed population of scores with μ = 25 and σ = 5. We have drawn a large number of random samples with a particular sample size of n = 10 from this population.

We want to know what the probability that a sample mean will be equal to or greater than 23.

First, what is the z-score for our sample mean of interest, 23?

Step 1

Given that a population distributed normally with mean 25 and standard deviation 5. Samples are drawn with sample size 10 from this population.

We want to know what the probability that the  mean of the sample means will be equal to or greater than 23.

P(Xbar > 23)

Step 2

Given µ = 25, σ = 5 .

Sample size n = 10.

In order to find out P(Xbar > 23) we need to find the Z score for Xbar =23.

Z score is the distance of a data point from its mean in terms of standard deviation, which can be calculated by the below mentioned formula.

Step 3

Mean of the sample = mean of the population = µ = 25.

Standard deviation of sample = Stadnard devaition of population/√sample size = (σ/√n), where &sig...

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