Question 10 (1 point) Weights of apples sold in a grocery store follow a normal

Question

Question 10 (1 point) Weights of apples sold in a grocery store follow a normal distribution with mean 150 grams and standard deviation 20 grams. In a random sample of 5 apples from the grocery store, what is the probability that zero apples are heavier than 175 grams? Carry 4 decimal places in intermediate calculations and report your final answer to 2 decimal places. Your Answer Answer Save Question 11 (1 point) Trees are distributed in a large forest according to a Poisson distribution with a rate of 0.2 per square meter. If we randomly select a circular area of the forest with a radius of 3 meters, what is the probability this area will contain 5 trees? (Area of a circleT Give your answer to 3 decimal places. Your Answer:

Explanation / Answer

#10.
mean = 150
std. dev. = 20

P(X > 175)
= P(z > (175 - 150)/20)
= P(z > 1.25)
= 0.1056 .. (uisng standard table/calculator)

probability that randomly selected apple is heavier than 175, p = 0.1056

P(X = 0) = (1-0.1056)^5 = 0.5723

Ans: 0.57

#11.
Area of circle = 22/7 * 3^2 = 28.2743 sq-meter

lambda = 28.2743 * 0.2 = 5.6549

Poisson's Distribution Formula:
P(X = 5) = (e^-5.6549) (5.6549^5) / 5! = 0.1687

Ans: 0.169

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