1. Suppose that the current distribution of weekly unemployment benefits paid ou

Question

1. Suppose that the current distribution of weekly unemployment benefits paid out is approximately normally distributed with a mean of $297 and a standard deviation of $74.42. Find the probability that a randomly selected American who is receiving unemployment benefits is receiving
a. More than $400 per week
b. Between $200 and $340 per week

2. According to the U.S. Department of Agriculture, the average American consumed 54.3 pounds (approximately seven gallons) of salad and cooking oils in 2008 (www.ers.usda.gov/data/foodconsumption). Suppose that the current distribution of salad and cooking oil consumption is approximately normally distributed with a mean of 54.3 pounds and a standard deviation of 14.5 pounds. What percentage of Americans’ annual salad and cooking oil consumption is a. less than 10 pounds b. between 40 and 60 pounds c. more than 90 pounds d. between 50 and 70 pounds

3. The lengths of 3 inch nails manufactured on a machine are normally distributed with a mean of 3 and a standard deviation of .009.

The nails are either shorter than 2.98 inches or longer than 3.02 inches are unusable. what of the nails produced by this machine are unusable?

Explanation / Answer

as from normal distribution ; z=(X-mean)/std deviation

1 a) P(X>400)=1-P(X<400)=1-P(Z<(400-297)/74.42)=1-P(Z<1.3840)=1-0.9168=0.0832

b)P(200<X<340)=P(-1.3034<Z<0.5778)=0.7183-0.0962=0.6221

2)a) P(X<10)=P(Z<(10-54.3)/14.5)=P(Z<-3.0552)=0.0011

b)P(40<X<60)=P(-0.9862<Z<0.3931)=0.6529-0.1620=0.4909

c) P(X>90)=1-P(X<90)=1-P(Z<2.4621)=1-0.9931=0.0069

d)P(50<X<70)=P(-0.2966<Z<1.0828)=0.8605-0.3834=0.4771

3)P(X<2.98)+P(X>3.02)=1-P(2.98<X<3.02)=1-P(-2.222<Z<2.222)=1-(0.9869-0.0131)=0.0263

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