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STAT 200 Week 4 Homework Problems

6.3.2 Find the z-score corresponding to the given area. Remember, z is distributed as the standard

normal distribution with mean of μ = 0 and standard deviation σ = 1.

a.)

b.)

c.)

d.)

e.)

The area to the left of z is 15%.

The area to the right of z is 65%.

The area to the left of z is 10%.

The area to the right of z is 5%.

The area between -z and z is 95%.

(Hint: draw a picture and figure out the area to the left of the -z.)

f.) The area between -z 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.

a.)

b.)

c.)

d.)

e.)

f.)

State the random variable.

Find the probability that a person in China has blood pressure of 135 mmHg or more.

Find the probability that a person in China has blood pressure of 141 mmHg or less.

Find the probability that a person in China has blood pressure between 120 and 125 mmHg.

Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?

What blood pressure do 90% of all people in China have less than?

6.3.10 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.

a.)

b.)

c.)

d.)

e.)

f.)

State the random variable.

Find the probability that the yearly rainfall is less than 100 mm.

Find the probability that the yearly rainfall is more than 240 mm.

Find the probability that the yearly rainfall is between 140 and 250 mm.

If a year has a rainfall less than 100mm, does that mean it is an unusually dry year?

What rainfall amount are 90% of all yearly rainfalls more than?

6.4.4 Annual rainfalls for Sydney, Australia are in table #6.4.6. (“Annual maximums of,” 2013). Can

you assume rainfall is normally distributed? (Hint: make a histogram or barchart)

Table #6.4.6: Annual Rainfall in Sydney, Australia

146.8

383

90.9

178.1

267.5

90.9

139.7

200.2

171.7

187.2

84.1

55.6

133.1

271.8

135.9

47.5

97.8

122.7

58.4

154.4

84.6

171.5

254.3

185.9

137.2

45.2

74.7

264.9

113.8

133.4

95.5

184.9

71.9

173.7

138.9

68.1

156.5

70.1

99.4

118.8

96.2

156.4

180

58

110.6

88

85

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. (Note: this problem is different from # 6.3.4)

a.)

b.)

c.)

d.)

e.)

State the random variable.

Suppose a sample of size 15 is taken. State the shape of the distribution of the sample mean.

Suppose a sample of size 15 is taken. State the mean of the sample mean.

Suppose a sample of size 15 is taken. State the standard deviation of the sample mean.

Suppose a sample of size 15 is taken. Find the probability that the sample mean blood

pressure is more than 135 mmHg.

f.) Would it be unusual to find a sample mean of 15 people in China of more than 135 mmHg?

Why or why not?

g.) If you did find a sample mean for 15 people in China to be more than 135 mmHg, what might

you conclude?

…

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