Question

Asked Mar 18, 2019

Please help!

Step 1

Given that a continuous variable of a population with mean = 11.46 and standard deviation = 6.15.

A sample of n = 78 is randomly picked

According to central limit theorem From any population with mean µ and standard deviation σ, random samples of large size (n) are chosen, then the distribution of sample means Xbar will be normal distribution with mean µ and standard deviation σ/√n.

So the distribution of Xbar (sample means) will be normal distribution with sample size n = 78 and the sample mean = 11.46 and sample standard deviation = 0.70 (rounded to two decimals) are shown below.

Step 2

We need to find the probability that mean of the sample of n = 78 is between 10.76 and 11.86.

So we need P( 10.76 < Xbar < 11.86...

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