Question

In a random sample of microwave​ ovens, the mean repair cost was ​$ and the standard deviation was ​$. Using the standard normal distribution with the appropriate calculations for a standard deviation that is​ known, assume the population is normally​ distributed, find the margin of error and construct a ​% confidence interval for the population mean μ. A 98​% confidence interval using the​ t-distribution was (687,913). Compare the results.

The margin of error of μ is:_______

Answer 1

Complete Question

In a random sample of 13 microwave ovens, the mean repair cost was $90.00 and the standard deviation was $15.20. Using the standard normal distribution with the appropriate calculations for a standard deviation that is known, assume the population is normally distributed, find the margin of error and construct a 98% confidence interval for the population mean u. A 98% confidence interval using the t-distribution was (78.7,101.3). Compare the results. The margin of error of u is

Answer:

The value is
`E = 11.65`

Explanation:

From the question we are told that

The sample is
`n = 13`

The sample mean is
`\= x = \$ 90`

The standard deviation is
`\sigma = \$ 15.20`

The lower limit of the 98% confidence interval is
`a = 78.7`

The upper limit of the 98% confidence interval is
`b = 101.3`

Generally the margin of error is mathematically represented as

`E = (b-a)/(2)`

=>
`E = ( 101.3 - 78 )/(2)`

=>
`E = 11.65`