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#44 Suppose that the miles-per-gallon (mpg) rating of passenger cars is a normal

ID: 3173295 • Letter: #

Question

#44     Suppose that the miles-per-gallon (mpg) rating of passenger cars is a normally distributed random variable with a mean and a standard deviation of 39.3 and 2.9 mpg, respectively. Use Table 1.

a.

What is the probability that a randomly selected passenger car gets more than 40 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

   Probability

b.

What is the probability that the average mpg of four randomly selected passenger cars is more than 40 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

   Probability

c.

If four passenger cars are randomly selected, what is the probability that all of the passenger cars get more than 40 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

   Probability

#44     Suppose that the miles-per-gallon (mpg) rating of passenger cars is a normally distributed random variable with a mean and a standard deviation of 39.3 and 2.9 mpg, respectively. Use Table 1.

a.

What is the probability that a randomly selected passenger car gets more than 40 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

   Probability

Explanation / Answer

a. P(x>40)=P(x>40-39.3/2.9)=P(z>0.24)=0.4052

b. P(xbar>40)=P(z>40-39.3/2.9/sqrt(4))=P(z>0.48)=0.3156

c. P(x=40)=P(z=40-39.3/2.9)=P(z=0.24)=0.5948

Required probability =0.5948^4=0.1252