Question

the number of chocolate chips in the 18 ounce bag of chips ahoy? chocolate chip cookies is approximately normally distributed with a mean of 1350 chocolate chips and a standard deviation of 218 chocolate chips

a) what is the probability that a randomly selected 18 ounce bag of chips ahoy contains more that 1600 chips

b)what is the probability that a randomly selected 18 ounce bag of chips ahoy contains less than 1200 chips

c)what is the probability that a randomly selected 18 ounce bag of chips ahoy contains between 1200 and 1600 chips

Answer 1

Given ,

= 1350 , = 218

We convert this to standard normal as

P( X < x) = P( Z < x - / )

a)

P( X > 1600) = P (Z > 1600 - 1350 / 218)

= P( Z > 1.1468)

= 0.1257

b)

P( X < 1200) = P( Z < 1200 - 1350 / 218)

= P( Z < -0.6881)

= 0.2457

c)

P( 1200 < X < 1600) = P( X < 1600) - P (X < 1200)

= P( Z < 1600 - 1350 / 218) - P( Z < 1200 - 1350 / 218)

= P( Z < 1.1468) - P( Z < -0.6881)

= 0.8743 - 0.2457

= 0.6286