17. An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. How large a sample is need it if we wish to be 98% confident that our sample mean will be within 4 hours of the true mean

A sample of at least 541 is needed if we wish to be 98% confident that our sample mean will be within 4 hours of the true mean.

Step-by-step explanation:

We are given that an electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours.

We have to find a sample such that we are 98% confident that our sample mean will be within 4 hours of the true mean.

As we know that the Margin of error formula is given by;

The margin of error =  

where, = standard deviation = 40 hours

            n = sample size

            = level of significance = 1 - 0.98 = 0.02 or 2%

Now, the critical value of z at ( = 1%) level of significance n the z table is given as 2.3263.

So, the margin of error =  

                   n = = 541.03 ≈ 541

Hence, a sample of at least 541 is needed if we wish to be 98% confident that our sample mean will be within 4 hours of the true mean.

10 - 75

step-by-step explanation:

there's nothing attached so it's most likely anything in that range.