During Spring 2013, a huge population of 17-year cicadas emerged from the ground on the East Coast of the United States. These prehistoric-looking bugs have red eyes, huge wings, and make noises as...

During Spring 2013, a huge population of 17-year cicadas emerged from the ground on the East Coast of the United States. These prehistoric-looking bugs have red eyes, huge wings, and make noises as loud as a lawnmower.33 Suppose the mean noise level is 90 decibels and the standard deviation is 15.6 decibels. During the cicada emergence in Virginia and other Southern states, a random sample of 40 locations was selected and the noise level (in decibels) was carefully measured.

 a. Find the probability distribution of the sample mean noise level.

b. Find the probability that the sample mean is less than 60 decibels, the level of moderate conversational speech.

 c. Find the probability that the sample mean is more than 110 decibels, the level of a passing train.

d. Find a value of n such that the probability that the sample mean is less than 93 decibels with probability 0.95.