The number of chocolate chips in an 18 ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips. See description for details.

Question

The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips.

1. What is the probability that a randomly selected bag contains between 1100 and 1400 chocolate chips?
2. What is the probability that a randomly selected bag contains fewer than 1000 chocolate chips?
3. What proportion of bags contains more than 1200 chocolate chips?
4. What is the percentile rank of a bag that contains 1425 chocolate chips?

Answer 1

For each of these, we'll be using the formula z = ^X-µ/_σ to determine the z-score, then using a table or calculator to determine the probability of being above, below, or between. For the last one, the percentage gets rounded down to the nearest whole percent. For the rest, round as desired.

1) z_L = ^1100-1252/₁₂₉ = -1.1783

z_U = ^1400-1252/₁₂₉ = 1.1473

P(-1.18 ≤ z ≤ 1.15) = 0.8749 - 0.119 = 0.7559 (table) or 0.755033 (calculator)

2) z = ^1000-1252/₁₂₉ = -1.9535

P(z ≤ -1.95) = 0.0256 (table) or 0.025381 (calculator)

3) z = ^1200-1252/₁₂₉ = -0.4031

P(z ≥ -0.4031) = 1 - 0.3446 = 0.6554 (table) or 0.656563 (calculator)

4) z = ^1425-1252/₁₂₉ = 1.3411

P(z ≤ 1.3411) = 0.91006

1425 has a 91st percentile rank.