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 1050 chocolate​ chips?

Answer 1

Solution :

Given that mean μ = 1252 , standard deviation σ = 129

(a) => P(1100 <= x <= 1500) = P(1099.5 < x < 1500.5)

= P((1099.5 - 1252)/129 < (x - μ)/σ < (1500.5 - 1252)/129)

= P(-1.1822 < Z < 1.9264)

= 0.8542

(b) => P(x < 1050) = P((x - μ)/σ < (1050 - 1252)/129)

= P(Z < -1.5659)

= 0.0582

(c) => P(x > 1200) = P((x - μ)/σ > (1200 - 1252)/129)

= P(Z > -0.4031)

= P(Z < 0.4031 )

= 0.6554

(d) P(x < 1050) = P((x - μ)/σ < (1050 - 1252)/129)

= P(Z < -1.5659)

= 0.0582

= 5.82%