Refer to exercise 6.35 where you are told that, for transformers build for heavy
ID: 3205951 • Letter: R
Question
Refer to exercise 6.35 where you are told that, for transformers build for heavy industry, the distribution of the number of sags per week has a mean of 353 and standard deviation of 30. Suppose that 60 of these transformers will be randomly selected and the sample mean number of sags per week, x, will be calculated. Use this information to answer the questions below. a) Describe the sampling distribution of?. Include the shape, mean, and standard deviation of the distribution in your description. Round any final values to 2 decimals, if necessary. b) What is the probability that this sample mean week will be greater than 345 sags per week? Round your answer to 4 decimals, if necessary.Explanation / Answer
a) as the sample size is large it will have a normal distribution.
the sampling distribution of xbar, will be centrerd at mean of population.
mean of Xbar =353
and std deviation of Xbar =(std deviation of population)/(n)1/2 =30/(60)1/2 =3.873
2)as from normal distribution, z score =(X-mean|)/std deviation
P(X>345) =1-P(X<345) =1-P(Z<(345-353)/3.873) =1-P(Z<-2.0656) =1-0.0194=0.9806