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 approximately normally distributed with mean 1252 and standard deviation 129 chips. (a) What is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips? (b) What is the probability that a randomly selected bag contains fewer than 1025 chocolate chips? (c) What proportion of bags contains more than 1175 chocolate chips? (d) What is the percentile rank of a bag that contains 1475 chocolate chips? Click the icon to view a table of areas under the normal curve. (a) The probability that a randomly selected bag contains between 1100 and 1500 chocolate chips is. (Round to four decimal places as needed.) (b) The probability that a randomly selected bag contains fewer than 1025 chocolate chips is. (Round to four decimal places as needed.) (c) The proportion of bags that contains more than 1175 chocolate chips is. (Round to four decimal places as needed.) (d) A b

Explanation / Answer

Mean = 1252

Standard deviation = 129

P(X < A) = P(Z < (A - mean) /standard deviation)

A) P(bag contains between 1100 and 1500 chocolate chips) = P(X < 1500) - P( X < 1100)

= P(Z < (1500 - 1252)/129) - P(Z < (1100 - 1252)/129)

= P(Z < 1. 92) - P(Z < -1.18)

= 0.9726 - 0.119

= 0.8536

B) P(X < 1025) = P(Z < (1025-1252)/129)

= P(Z < -1.76)

= 0.0392

C) P(X > 1175) = 1 - P(X < 1175)

= 1 - P(Z < (1175 - 1252)/129)

= 1 - P(Z < -0.60)

= 1 - 0.2743

= 0.7257

D) P(X < 1475)

= P(Z < (1475-1252)/129)

= P(Z < 1. 73)

= 0.9581

So, 1475 chocolate chips is in the 96th percentile

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