5.5-4. Let X equal the weight of the soap in a "6-pound" box. Assume that the distribution of X is N(6.05. 0.0004). (a) Find P(X < 6.0171). (b) If nine boxes of soap are selected at random from the production line, find the probability that at most two boxes weigh less than 6.0171 pounds each. HINT: Let Y equal the number of boxes that weigh less than 6.0171 pounds. (c) Let X be the sample mean of the nine boxes. Find P(X ≤ 6.035).

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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I only need help with part (a) and (c) on this Intro to probability and statistics homework problem. Make sure your handwriting is neat and readable.

 

5.5-4. Let X equal the weight of the soap in a "6-pound"
box. Assume that the distribution of X is N(6.05, 0.0004).
(a) Find P(X < 6.0171).
(b) If nine boxes of soap are selected at random from the
production line, find the probability that at most two
boxes weigh less than 6.0171 pounds each. HINT: Let Y
equal the number of boxes that weigh less than 6.0171
pounds.
(e) Let X be the sample mean of the nine boxes. Find
P(X ≤ 6.035).
Transcribed Image Text:5.5-4. Let X equal the weight of the soap in a "6-pound" box. Assume that the distribution of X is N(6.05, 0.0004). (a) Find P(X < 6.0171). (b) If nine boxes of soap are selected at random from the production line, find the probability that at most two boxes weigh less than 6.0171 pounds each. HINT: Let Y equal the number of boxes that weigh less than 6.0171 pounds. (e) Let X be the sample mean of the nine boxes. Find P(X ≤ 6.035).
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