Question

The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips.

(a) What is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips, inclusive?

(b) What is the probability that a randomly selected bag contains fewer than 1050 chocolate chips?

(c) What proportion of bags contains more than 1200 chocolate chips?

(d) What is the percentile rank of a bag that contains 1475 chocolate chips?

Answer #1

solution:-

given that mean = 1252 chips and standard deviation = 129 chips

(a) P(1100 < x < 1500)

=> P((1100-1252)/129 < z < (1500-1252)/129)

=> P(-1.18 < z < 1.92)

=> P(z < 1.92) - P(z < -1.18)

=> 0.9726 - 0.1190

=> 0.8536

(b) P(x < 1050)

=> P(z < (1050-1252)/129)

=> P(z < -1.57)

=> 1 - P(z < 1.57)

=> 1 - 0.9418

=> 0.0582

(c) P(x > 1200)

=> P(z > (1200-1252)/129)

=> P(z > -0.40)

=> P(z < 0.40)

=> 0.6554

(d) the percentile rank of a bag that contains 1475 chocolate
chips

=> P(X < 1475)

=> P(z < (1475-1252)/129)

=> P(z < 1.73)

=> 0.9582

=> 96 percentile

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