In a sample of 60 electric motors, the average efficiency

Solution 10E

Step1 of 6:

Let us consider a random variable X it represents the efficiency of electric motors. Here random variable X follows normal distribution with mean standard deviation and n = 60.

That is

The probability density function of normal distribution is given by

, .

Where,

x = random variable

= mean of X

= variance of X

= standard deviation os X

= mathematical constant and its value is 3.14

Here our goal is:

a). We need to find a 95% confidence interval for the mean efficiency.

b). We need to find a 99.5% confidence interval for the mean efficiency.

c). We need to find the confidence level of the interval (84.63, 85.37).

d). We need to find a 95% confidence interval specifies the mean to within

e). We need to find a 99.5% confidence interval specifies the mean to within

Step2 of 6:

a).

Here we have to find 95%  CI, let us take .

Now,

   = 0.025

Z-scores(are to the right) is given by

  is obtained from standard normal table(area under normal curve). In standard normal table we have to see where 0.9750 value falls, it falls in row 1.9 under column 0.06.

Hence,

  95% confidence interval for the mean efficiency is given by

(84.4939, 85.5060)

Hence, 95% confidence interval for the mean efficiency is (84.4939, 85.5060).