The number of chocolate chips in an 18 ounce bag of chocolate chip cookies is ap

Question

The number of chocolate chips in an 18 ounce bag of chocolate chip cookies is approximate normally distributed with a mean 1252 chips and standard deviation 129 chips What is the probability that a randomly selected bag contains between 1000 and 1400 chocolate chips, inclusive' What is the probability that a randomly selected bag contains fewer than 1000 chocolate chips' What proportion of bags contains mote than 1175 chocolate chips? What is the percentile rank of a baa that contains 1000 chocolate chips?

Explanation / Answer

Answer to the question)

mean M = 1252

Standard deviation s = 129

.

Part a)

P(1000 < x < 1400) = P( x< 1400) - P( x< 1000)

.

P(x < 1400) = P(z < (1400-1252)/129)

P(x < 1400) = P(z < 1.15) = 0.8749

.

P(x < 1000) = P( z < (1000-1252)/129)

P(x < 1000) = P(z < -1.95) = 0.0256

.

P(1000 < x < 1400) = 0.8749 -0.0256

P(1000 < x < 1400) =0.8493

.

Part b)

P(x < 1000) = P(z < (1000-1252)/129)

P(x < 1000) = P(z < -1.95) = 0.0256

.

Part c)

P( x> 1175) = 1 - P(x < 1175)

.

P(x < 1175) = P(z < (1175-1252)/129)

P(x < 1175) = P(z < -0.60) = 0.2743

.

P(x > 1175) = 1 - 0.2743

P( x > 1175) = 0.7257

.

Part d)

We know that P(X < 1000) = 0.0256

thus the percentile rank is ; 0.0256*100

Percentile rank = 2.56%

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