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Finding percent of scores and probability

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1. A recent survey of 1000 adults shows that 58% believe airplanes to be the safest mode of travel.
Construct a 99% confidence interval for the proportion of adults who think airplanes are the safest mode of transportation.

2. An aptitude test has a mean score of 80 and a standard deviation of 5. The population of scores is normally distributed.

a. What percent of tests has scores over 90
b. What raw score corresponds to the 70th percentile?

3. A major theatre chain interviewed 35,900 movie customers nationwide and recorded the following results:

FILM Preference Under 16 16 - 20 years-old 21 - 30 years-old 31 - 50 years-old Over 50 years old
DRAMA 250 500 3,000 5,500 2,500
COMEDY 2,000 500 2,500 3,500 2,300
ACTION 1,000 1,000 2,000 1,250 1,100
HORROR 500 3,000 2,500 250 750
TOTAL 3,750 5,000 10,000 10,500 6,650

If one movie customer were randomly selected , then determine the following:

a) the probability that the customer would be over 20 years-old?
b) the probability that the customer would be over 30 years-old and NOT prefer horror films.
c) the probability that the customer would be over 30 and prefer drama or comedy.
d) the probability that the customer would be either under 21 years-old or prefer drama.
e) the probability that the customer would NOT like comedies.

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The solution finds a percent of test scores and the probability of customers of a movie theater.

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