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#### Naval Public Graduate School Midterm exam q1: The charge-time of a laptop battery is normally distributed with mean 250 minutes and standard deviation 30 minutes

###### Statistics

Naval Public Graduate School Midterm exam

q1: The charge-time of a laptop battery is normally distributed with mean 250 minutes and
standard deviation 30 minutes. Suppose we test one such battery.

a. Find the probability that the time required to charge the battery is less than 5 hours.
b. Find the 95% percentile of the time needed to charge the battery (i.e., the minimum time needed so that the probability of a battery being fully charged is 0.95).

q2: There are four dice with varying numbers on each face:

Die A. has 1 2 4 5 6 7
Die B. has 4 4 4 4 4 4
Die C. has 2 6 2 6 2 2
Die D. has 3 5 3 5 3 5

You and three friends play a game where you each roll one of the dice and the highest number wins. You get first pick from the dice.

Question: Which die should you choose in order to maximize your chance of winning?

q3: A company that manufactures video cameras produces a basic model and a deluxe model. Over the past year, 40% of the cameras sold have been of the basic model. Of those buying the basic model, 30% purchase an extended guarantee, whereas 50% of all deluxe purchasers do so. If you learn that a randomly selected purchaser has an extended warranty, how likely is it that she has a basic model?

q4: Gophers are distributed in a large field according to a Poisson distribution with rate lambda=.2 per square yard. How large should the radius R of a circular sampling region be taken so that the probability of finding at least one in the region equals 0.99?

q5: Consider a well shuffled deck of cards, from which 5 cards are drawn.
a. Find the probability that you get three cards of hearts, and two cards of spades.
b. Find the probability that you get three cards of the same suit, and two cards with the same suit (but different than the one of the three other cards).

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