You may need to use the appropriate appendix table or technology to answer this question.The average lifetime of a light bulb is 3,000 hours with a standard deviation of 714 hours. A simple random sample of 36 bulbs is taken.

(a)What is the expected value (in hours) of the sampling distribution of x? hours

What is the standard deviation (in hours) of the sampling distribution of x? hours

What is the shape of the sampling distribution of x?:

bimodalskewed, to the right,skewed, to the left, multimodal, or normal

(b)What is the probability that the average life in the sample will be between 2,630.53 and 2,804.75 hours? (Round your answer to four decimal places.)

(c)What is the probability that the average life in the sample will be greater than 3,217.22 hours? (Round your answer to four decimal places.)

(d)What is the probability that the average life in the sample will be less than 3,120.97 hours? (Round your answer to four decimal places.)