Question: Please show complete steps. Suppose the length a cat takes a nap (the length of a cat nap) has a population mean of 3 hours,

Please show complete steps.

Suppose the length a cat takes a nap (the length of a cat nap) has a population mean of 3 hours, with a population standard deviation 1.75 hours. Assume the length of a cat nap is normally distributed.

a) Find the probability that a randomly selected cat takes a nap over 4 hours length.

b) If a cat has been napping for 2 hours, what is the probability that they nap at most an additional 1.5 hours?

c) A cat sleeps 4.35 hours. What percentile does this value represent? (Answer in 2 decimal places. Ex: If you find 12.34 percentile, report 12.34)

d) Find the probability that the average nap times of 4 randomly selected cats is between 2 and 3 hours.

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