The breakdown voltage of a randomly chosen diode of a certain type of known to be normally distributed with mean 40 V and standard deviation 1.5 V.

a. What is the probability that the voltage of a single diode is between 39 and 42?

b. What value is such that only 15% of all diodes have voltages exceeding that value ? what percentile does this value represent for the breakdown voltage distribution ?

c. A random sample of size 9 is drawn from the above normal distribution. let x̅ be the random sample mean.

i. Give the sampling distribution of x̅ with its mean and variance

ii. Obtain P(39.5 < x̅<41.0)