Question

sing the make of a car in at least three of the five families? Use Binomial Table 2. If Z is a standard normal random variable find the following probabilities (Standard Table is in the Appendix and is also posted under Course Document) a. P(ZS-1.77) b. P(-2.88 SZ S-2.15) 3. Studies show that gasoline use for compact cars sold in the United States is normally distributed, with mean use of 25.5 miles per gallon (mpg) and a standard deviation of 4.5 mpg. a. What percentage of compact cars obtain 30 or more mpg? b. In times of scarce energy resources a competitive advantage is given to automobile manufacturers who can produce a car obtaining substantially better fuel economy than the competitor s cars. If a manufacturer wishes to develop a compact car that outperform 95% of the current compacts in fuel economy. what must be the gasoline mileage for the new car?

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Answer 1

2.

P(Z<=1.77) = 0.9616 [From Z standard table]

P( -2.88 <= Z <= -2.15) = P(Z <= -2.15) - P(Z <= -2.88) = 0.0158-0.0020 = 0.138

3.

b) The geven statement can be expressed in lerons of probability as P(Z > a) =10.95 - 005 We're to find the value of 'a', Plz > a) = 0.5 - P(oczca) in 0.05 = 0.5 - PloLzea). Ploczta) = 0.5 – 0.05 = 0.45 From tables standard normal curse we get the as 0.45 when a = 1.645 in, PCOLZL 1.645) = 0.45 area > a = 1.645 ie, 3 = 1.645 - 1.645 x-p o . x-25.5 = 1:645 4.5 + 25.5 a = 1.645X4.5 a = 32.90 new car will be more than 32.9. ie, the mileage for

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