Question

The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 420 grams and a standard deviation of 24 grams. Find the weight that corresponds to each event. (Use Excel or Appendix C to calculate the z-value. Round your final answers to 2 decimal places.) a. Highest 20 percent b. Middle 60 percent to c. Highest 80 percent d. Lowest 15 percent.

Answer 1

Answer and Step-by-step explanation:

Round your final answers to 2 decimal places

μ = 420

σ = 24

a. Highest 20 percent

P (Z > a-420/24) = 0.20

For a highest 20%, according to the table attached, we have to find the z score for 0.30 (0.5 - 0.2)

P(0 < Z < 0.84) = 0.3

a-420/24 = 0.84

a-420 = 20.16

a = 20.16 + 420 = 440.16

weight 440.16

b. Middle 60 percent

P (0 < Z < b-420/24) = 0.3

b = 440.16

P (c-420/24 < Z < 0) = 0.3

c-420/24 = -0.84

c-420 = -20.16

c = 399.84

Weight from 399.84 to 440.16

c. Highest 80 percent

P (d-420/24 < Z < 0) = 0.3

d-420/24 = -0.84

d-420 = -20.16

d = 399.84

d. Lowest 15 percent

P(e-420/24 < Z < 0) = 0.35

e-420/24 = -1.04

e-420 = -29.76

e = 390.24