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 1000 and 1400 chocolate​ chips, inclusive ​(b) What is the probability that a randomly selected bag contains fewer than 1125 chocolate​ chips ​(c) What proportion of bags contains more than 1225 chocolate​ chips ​(d) What is the percentile rank of a bag that contains 1425 chocolate​ chips

Answer 1

a)

P(1000 < X < 1400)

= P(-1.9535 < Z < 1.1473)

= P(Z < 1.15) - P(Z < -1.95)

= 0.8749 - 0.0256

= 0.8493

b) P(X < 1125)

= P(Z < -0.98)

= 0.1635

c) P(X > 1225)

= P(Z > -0.21)

= 1 - P(Z < -0.21)

= 1 - 0.4168

= 0.5832

d) P(X < 1425)

= P(Z < 1.34)

= 0.9099

= 90.99%