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  $E = 11.65$

Step-by-step 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

        $E = \frac{b-a}{2}$

=>    $E = \frac{ 101.3 - 78 }{2}$

=>    $E = 11.65$