Seventy percent of the bicycles sold by a certain store are mountain bikes. Amon

Question

Seventy percent of the bicycles sold by a certain store are mountain bikes. Among 100 randomly selected bike purchases, find the probabilities below. (Round your answers to four decimal places.)

(a) What is the approximate probability that at most 85 are mountain bikes?


(b) What is the approximate probability that between 60 and 85 (inclusive) are mountain bikes?


(c) What is the approximate probability that more than 90 are mountain bikes?


(d) What is the approximate probability that at most 30 are not mountain bikes?

Explanation / Answer

Probability that a random bike is a mountain bike p = 0.7.

Number of bikes n = 100.

X ~ Binom(100, 0.7).

Using Binomial tables,

(a) P(X <= 85) = 0.9998.

(b) P(60 <= X <= 85) = P(X <= 85) - P(X < 60)

= 0.9998 - 0.0125

= 0.9873.

(c) P(X > 90) = 0.0000.

(d) P(X <= 30)' = P(X >= 70) = 0.5491.

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