Question

The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 350 grams and a standard deviation of 11 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

Part a)

P ( X > ? ) = 1 - P ( X < ? ) = 1 - 0.1 = 0.9
Looking for the probability 0.9 in standard normal table to calculate critical value Z = 1.28

1.28 = ( X - 350 ) / 11
X = 364.08
P ( X > 364.08 ) = 0.1

Part b)

P ( a < X < b ) = 0.5
Dividing the area 0.5 in two parts we get 0.5/2 = 0.25
since 0.5 area in normal curve is above and below the mean
Area below the mean is a = 0.5 - 0.25
Area above the mean is b = 0.5 + 0.25
Looking for the probability 0.25 in standard normal table to calculate critical value Z = -0.67
Looking for the probability 0.75 in standard normal table to calculate critical value Z = 0.67

-0.67 = ( X - 350 ) / 11
a = 342.63
0.67 = ( X - 350 ) / 11
b = 357.37
P ( 342.63 < X < 357.37 ) = 0.5

part c)

P ( X > ? ) = 1 - P ( X < ? ) = 1 - 0.8 = 0.2
Looking for the probability 0.2 in standard normal table to calculate critical value Z = -0.84

-0.84 = ( X - 350 ) / 11
X = 340.76
P ( X > 340.76 ) = 0.8

Part d)

P ( X < ? ) = 10% = 0.1
Looking for the probability 0.1 in standard normal table to calculate critical value Z = -1.28

-1.28 = ( X - 350 ) / 11
X = 335.92
P ( X < 335.92 ) = 0.1