In a sample of 80 light bulbs, the mean lifetime was 1217 hours with a standard deviation of 52 hours. a. Find the 95% confidence interval for the mean lifetime of this type of bulb. Justify the reason you chose the distribution used to construct the confidence interval. b. How many light bulbs must be sampled so that a 95% confidence interval will specify the mean lifetime to within + 8 hours?

Complete Question

In a sample of 80 light bulbs, the mean lifetime was 1217 hours with a standard deviation of 52 hours. a. Find the 95% confidence interval for the mean lifetime of this type of bulb. Justify the reason you chose the distribution used to construct the confidence interval. b. How many light bulbs must be sampled so that a 95% confidence interval will specify the mean lifetime to within ?

a

The reason why a normal distribution was chosen is because the sample size is large enough that is    

b

Step-by-step explanation:

From the question we are told that

    The sample size is  n  =  80  

    The sample mean is  

     The standard deviation is  

From the question we are told the confidence level is  95% , hence the level of significance is    

=>  

Generally from the normal distribution table the critical value  of   is  

Generally the margin of error is mathematically represented as  

=>    

=>    

Generally 95% confidence interval is mathematically represented as  

=>  

=>  

Generally the sample size is mathematically represented as  

Here  E =  8

=>  

=>  

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^

30 units^2

step-by-step explanation:

area is l × w

the length is 3

and the width is 10

3 × 10= 30 units squared