# 1. A survey was conducted asking people if they thought they were overweight

August 30, 2017

Question

1. A survey was conducted asking people if they thought they were overweight. Participants were randomly selected. Data were analyzed by how many participants in each age groups were male or female.

18-21

22-29

30-39

40-49

50-59

60+

Female

73

255

245

136

138

202

Male

11

20

33

16

27

49

What is the probability that the randomly selected participant is someone 60 or overand is female?

I am not interested in males or in anyone under 22 or over 59. What is the probability that the randomly selected participant is someone I am interested in?

2. Twenty students are eligible for a GT/LD program in my school district. A simple random sample of five is selected.

How many different random sample selections are possible?

What is the probability of each simple random sample?
3. In a study of families with children with disabilities, groups of 5 US households were randomly selected. In the table below, the random variablex represents the number of households among 5 that had a child with a disability living there.

X

P(x)

0

0.02

1

0.15

2

0.29

3

0.26

4

0.16

5

0.12

a) Is this a probability distribution?

b) What is the mean?

c) What is the standard deviation?

4. Ten peas are generated from parents having the green/yellow pair of genes so there is a

75% probability that an individual pea will have a green pod. Find the probability that among the 10 offspring peas,at least 9 have green pods. Is this unusual? Explain.

5. (2 points) My niece is an auditor. She analyzed my checking accounts by randomly selecting five checks from my account. They were for the following amounts:

\$115.00 \$188.00 \$134.83 \$217.60 \$142.94

a. Find the mean

b. Find the median

c. Find the range

d. Find the standard deviation

e. Find the variance

f. Are any of the sample values unusual?

g. What is the level of measurement of the data?

h. If she sampled the last five checks I wrote, what type of sampling would have been used?

i. I wrote 134 checks that year of which she sampled five. Estimate the total value of all checks written that year.

6. Assume womenâ€™s ring sizes are normally distributed with a mean of 6 and a standard deviation of 1.0.

a. If one woman is randomly selected, find the probability that her ring size is < 6.2

b. If 100 women are randomly selected, find the probability that the mean ring size is < 6.2

c. A jeweler sees part b. and decides that all rings should be made was calculated for each sample.

a. What is the approximate shape of the distribution of the sample means?

b. What is the expected mean of the sample means?

c. What is the expected standard deviation of the sample means?

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