For this question, I kow how to do all parts... except Part D. Please help me an

Question

For this question, I kow how to do all parts... except Part D. Please help me answer and explain Part D (in detail!).

2. (15 marks) A large population of seeds of the princess beans Phaseotus vulgaris is to be sampled. The weight of the seeds in the population follow a normal distribution with mean -500 mg, and standard deviation -120 mg. a) What percentage of seeds have a weight 520 mg or more? (b) Suppose now that a random sample of four seeds is to be weighted. What is the proba- bility that the mean weight of the four seeds will be grater than 550 mg? 45 seeds will be between 480 mg and 520 mg? distributed? Explain why or why not in each case. c) We select 45 seeds at random. What is the probability that the average weight of these (d) Do the answers of parts (b) and (c) change if the weight of a seed is not normally

Explanation / Answer

d) part (b) answer will change (Using CENTRAL LIMIT THEOREM) Since the sample size is less than 30(i.e. 4).

but the part(c) answer will remain the same (Using CENTRAL LIMIT THEOREM) because the sample size is 45 which is greater than 30.

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