Statistics- A large shipment of Granny Smith apples arrives at a grocery store

QUESTION

want to make sure i did these right before i submit themA large shipment of Granny Smith apples arrives at a grocery store. Weights of the apples are known to follow a normal distribution with mean 152 grams and standard deviation 16 grams.(a) You select a random sample of three apples. Can you calculate the probability that the mean weight of the apples in the sample is less than 141.28?(b) If you select a random sample of 40 apples, what is the probability that the mean weight of the apples in the sample is between 144.89 and 155.42?(c) If you select a random sample of 50 apples, what is the probability that the total weight of the apples is greater than 7688.25 grams?(d) Are the probabilities you calculated in (b) and (c) exact or approximate? Explain.The amount of a waiter’s tips follows some right-skewed distribution with mean $6.62 and standard deviation $3.55.(a) We take a random sample of three of the waiter’s customers. Can you calculate the probability that the mean tip for these customers is less than $9.43?(b) If we take a random sample of 35 of the waiter’s customers, what is the probability that the mean tip for these customers is greater than $6.13? (c) If we take a random sample of 45 of the waiter’s customers, what is the probability that the mean tip for these customers is between $5.08 and $6.87? (d) Are the probabilities you calculated in (b) and (c) exact or approximate? Explain.

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