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