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78) Given the binomial distribution function P(x) = C 6,x (.7) x (.3) 6-x , find:

a) the mean

b) the standard deviation

79) A certain lawyer wins 80% of all her cases.

a) What then is the probability that she will win exactly 2 of her next 5 cases?

b) What is the probability that she will win at least 2 of her next 5 cases?

80) A normal distribution has mean 200 and standard deviation 50. Find the area under the normal curve from

the mean to 224.

81) The duration of routine operations in a certain hospital has approximately a normal distribution with a mean

of 72 minutes and a standard deviation of 9 minutes. What percentage of operations last less than 68

minutes?

82) Given the following data set, what actual percentage of the measurements lies within one standard deviation

of the mean?

83) A fair coin is tossed 14 times. What is the probability of obtaining exactly 12 heads? Express the answer both

in terms of C n,k and as a four-place decimal.

84) A botanist wants to grow a rare plant in his greenhouse. The probability that a given bulb will mature is .42.

Suppose 6 bulbs are planted.

a) Write the probability function defining this distribution.

b) What is the probability that 3 or more bulbs will mature? (Round your answer to three decimal places.)

85) A manufacturing process produces, on average, 1% defective items. The company ships 16 items in each box.

Compute the mean and standard deviation if a success on a single trial (inspecting one item in a box) is

finding the item defective.

86) A company guarantees customer satisfaction on the purchase of a product, or the company will refund the

purchase price of the product. Previous experience has shown that 10% of the purchases are returned. What

is the probability that no more than 1 of the next 7 purchases will be returned?

87) The life expectancy (in hours) of a fluorescent tube is normally distributed with mean 7,000 and standard

deviation 1,000.

a) Find the probability that a tube lasts for more than 8,900 hours.

b) Find the probability that a tube lasts for 8,000 hours.

c) Find the probability that a tube lasts less than 8,000 hours.

88) A pharmaceutical laboratory claims that a drug it produces causes serious side effects in 60 people out of

1,000 on the average. A research team administers the drug to 400 randomly chosen people. Assuming the

laboratory's claim is correct, use the normal approximation to the binomial distribution to find the probability

that 19 or fewer people experience serious side effects.

89) The duration of routine operations in a certain hospital has approximately a normal distribution with an

average of 130 minutes and a standard deviation of 15 minutes. What percentage of operations last longer

than 150 minutes?

Math Exam Final Review Worksheet With Answer Key - M118, Indiana University Southeast Page 8