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the number of hamburgers A fast-food restaurant sells take-home hamburgers. It is measured that sold per day follows a normal distribution with mean 150 and standard deviation 30. a. What is the probability that the restaurant sells more than 160 hamburgers in a day? b. What is the probability that the restaurant sells between 130 and 160 hamburgers in a day? c. The probability is 0.1 that the restaurant sells less than how many hamburgers in a day?
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Answer #1

Let X is a random variable shows the number of hamburgers restaurant sells in day. Here we have

, 150, σ = 30

(a)

The z-score for X = 160 is

X-μ 160-150 30 0.33

The required probability is

P(X > 160) 1-P(X < 160)-1-P(z < 0.33)-1-0.6293-0.3707

Answer: 0.3707

(b)

The z-score for X = 130 is

X-μ 130-150 30

The required probability is

P(130 X 160)P(X 160)- P(X 130)P0.33)- Pz -0.67) 0.3779

Answer: 0.3779

(c)

Here we need z-score that has 0.10 area to its left. The z-score -1.28 has 0.10 area to its left. The required X is

X-150 30 X-μ

X-150 1.2830

X-111.6

Answer : 112 hamburgers in a day

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