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STAT 200 Week 4 Homework Problems

6.1.2

a.)State the random variable.

b.)Find the height of this uniform distribution.

c.)Find the probability of waiting between four and five minutes.

d.)Find the probability of waiting between three and eight minutes.

e.)Find the probability of waiting five minutes exactly.

6.3.2

Find the z-score corresponding to the given area.Remember, z is distributed as the standard normal distribution with mean of and standard deviation .

a.)The area to the left of z is 15%.

b.)The area to the right of z is 65%.

c.)The area to the left of z is 10%.

d.)The area to the right of z is 5%.

e.)The area between and z is 95%.(Hint draw a picture and figure out the area to the left of the .)

f.)The area between and z is 99%.

6.3.4

According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg (Kuulasmaa, Hense & Tolonen, 1998).Assume that blood pressure is normally distributed.

6.3.8

A dishwasher has a mean life of 12 years with an estimated standard deviation of 1.25 years (“Appliance life expectancy,” 2013).Assume the life of a dishwasher is normally distributed.

6.3.10

The mean yearly rainfall in Sydney, Australia, is about 137 mm and the standard deviation is about 69 mm (“Annual maximums of,” 2013).Assume rainfall is normally distributed.

6.4.4

Annual rainfalls for Sydney, Australia are given in table #6.4.6. (“Annual maximums of,” 2013).Can you assume rainfall is normally distributed?

Table #6.4.6: Annual Rainfall in Sydney, Australia

146.8

383

90.9

178.1

267.5

95.5

156.5

180

90.9

139.7

200.2

171.7

187.2

184.9

70.1

58

84.1

55.6

133.1

271.8

135.9

71.9

99.4

110.6

47.5

97.8

122.7

58.4

154.4

173.7

118.8

88

84.6

171.5

254.3

185.9

137.2

138.9

96.2

85

45.2

74.7

264.9

113.8

133.4

68.1

156.4

6.5.2

A random variable is normally distributed.It has a mean of 245 and a standard deviation of 21.

6.5.4

According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg (Kuulasmaa, Hense & Tolonen, 1998).Blood pressure is normally distributed.

6.5.6

The mean cholesterol levels of women age 45-59 in Ghana, Nigeria, and Seychelles is 5.1 mmol/l and the standard deviation is 1.0 mmol/l (Lawes, Hoorn, Law & Rodgers, 2004).Assume that cholesterol levels are normally distributed.

6.5.8

A dishwasher has a mean life of 12 years with an estimated standard deviation of 1.25 years (“Appliance life expectancy,” 2013).The life of a dishwasher is normally distributed.Suppose you are a manufacturer and you take a sample of 10 dishwashers that you made.