Question

The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 390 grams and a standard deviation of 9 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 10 percent
b.	Middle 50 percent		to
c.	Highest 80 percent
d.	Lowest 10 percent

Answer 1

Given that,

mean = = 390

standard deviation = = 9

(a)

P(Z < 1.28) = 0.90

z = 1.28

Using z-score formula,

x = z * +

x = 1.28 * 9 + 390 = 401.52

Weight = 401.52

(b)

Middle 50% has the z values : -0.67 and +0.67

x = -0.67 * 9 + 390 = 383.97

x = +0.67 * 9 + 390 = 396.03

Weight : 383.97 to 396.03

(c)

P(Z < -0.84) = 0.20

Using z-score formula,

x = z * +

x = -0.84 * 9 + 390 = 382.44

Weight = 382.44

(d)

P(Z < -1.28) = 0.10

z = -1.28

Using z-score formula,

x = z * +

x = -1.28 * 9 + 390 = 378.48

Weight = 378.48