Suppose an interval estimate for the population mean was 62.84 to 69.46. the population standard deviation was assumed to be 6.50, and a sample of 100 observations was used. the mean of the sample was: a. 56.34 b. 62.96 c. 6.62 d. 66.15

Because the confidence interval is defined as

The best option is : D. 66.15

Step-by-step explanation:

Previous concepts

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

represent the sample mean  (variable of interest)

population mean

represent the population standard deviation  

n=100 represent the sample size  

Assuming the X follows a normal distribution  

The sample mean is distributed on this way:

The confidence interval on this case is given by:

(1)

We have a confidence interval given (62.84, 69.46). W ecan find the margin of error for this interval with this:

With the margin of error we can find the sample mean with this:

Because the confidence interval is defined as

The best option is : D. 66.15