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**

4. The number of chocolate chips in an 18-ounce bag of Chips
Ahoy! cookies is approximately normally distributed with a mean of
µ = 1262 chips and standard deviation σ = 188 chips. Source: Brad
Warner and Jim Rutledge, Chance, 12(1): 10-14, 1999
(a) (3 points) What is the probability that a randomly selected
18-ounce bag of Chips Ahoy! contains between 1000 and 1400
chocolate chips, inclusive? Round your answer to 4 decimal places.
Problem 4 continued:
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