Question

The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 385 grams and a standard deviation of 8 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 30 percent b. Middle 70 percent to c. Highest 90 percent d. Lowest 20 percent

Answer 1

Solution :

mean = = 385

standard deviation = = 8

Using standard normal table,

(a)

P(Z > z) = 30%

1 - P(Z < z) = 0.30

P(Z < z) = 1 - 0.30 = 0.70

P(Z < 0.52) = 0.70

z = 0.52

Using z-score formula,

x = z * +

x = 0.52 * 8 + 385 = 389.16

Weight = 389.16

(b)

Middle 70% has z values : -1.04 and 1.04

x = -1.04 * 8 + 385 = 376.68

Weight = 376.68

x = 1.04 * 8 + 385 = 393.32

Weight = 393.32

Middle 70% weights are (376.68 , 393.32)

(c)

(Z > z) = 90%

1 - P(Z < z) = 0.90

P(Z < z) = 1 - 0.90 = 0.10

P(Z < -1.28) = 0.10

z = -1.28

Using z-score formula,

x = z * +

x = -1.28 * 8 + 385 = 374.76

Weight = 374.76

(d)

P(Z < -0.84) = 0.20

z = -0.84

Using z-score formula,

x = z * +

x = -0.84 * 8 + 385 = 378.28

Weight = 378.28