Statistics and Probability Answers

A health care professional wishes to estimate the birth weights of infants. How large a sample she needs to select if she desires to be 95% confident that the true mean is within 3 (+/-3 gms) of the sample mean? The standard deviation of the birth weights is known to be 105 gms.

1. A survey was conducted among 960 people on their opinion about President Obama’s health care proposal. The following information was collected:
a). There were 560 Democrats and 400 Republicans
b). Among the Democrats, 400 supported the President’s health care proposal and the rest didn’t.
c). Among the Republicans, 200 supported the President’s health care proposal and the rest didn’t.
Answer the following questions: (18 points)
Suppose a person is selected randomly from these 960 people
i). What is the probability that the person is a Democrat?
ii). What is the probability that the person is a Republican who doesn’t support the President’s proposal?
iii). What is the probability that the person is a Republican or the person supports the President’s proposal?
iv). What is the probability that the person supports the President’s proposal knowing that the person is a Democrat?
v). Are “being a Democrat” and “supporting the President’s proposal” independent events?
vi). Are “being a Democrat” and “supporting the President’s proposal” mutually exclusive events?

The acreage (in thousands of acres) of the 39 U.S. National Parks is shown here. Construct a frequency distribution for the data using eight classes.

41 66 233 775 169
36 338 233 236 64
183 61 13 308 77
520 77 27 217 5
650 462 106 52 52
505 94 75 265 402
196 70 132 28 220
760 143 46 539

According to a reactor ding to government data, the probability that an adult was never in a museum is 15%. In a random survey of 10 adults, what is the probability that at least eight were in a museum?

A machine needs 2 of its gears replaced. You find 2 gears, one manufactured 5 years ago and the other manufactured 10 years ago. The specifications sheet says that the chance of failure is 5% after 5 years and increases to 8% after 10 years. If the gears on the machine are in no way linked to each other, what are the chances that both will fail?

past experience shows that the probablilty that a sales person will exceed target sales is 74%, gven that they exceeded in the previous year. Suppose the probability of a salesperson exceeding target sales within a given year is 53%. What is the probability that the salesperson will exceed target sales two years in a row?

For each of the situations ( #5a-e below) construct the 95% confidence interval estimate to the population. Assume that the results are based on a representative sample of Canadians. Express the estimate in a sentence.

a) The average age of the 925 respondents was 37.3 years with a standard deviation of 2.9.
b) Of the 799 respondents questioned, 126 identified themselves as atheist.
c) Of the 1220 respondents for whom we have information, 222 said that they had
been divorced at least once.
d) Four hundred and thirty two of the 668 respondents questioned said that they
are concerned about the environment.
e) The average number of children for the 945 respondents for which we have
information was 1.67 with a standard deviation of .94.

I surveyed each house on the block to determine how much we are spending on Halloween
treats. The distribution below represents the results in dollars.
$Spent f
50-59 1
40-49 2
30-39 5
20-29 12
10-19 7
0-9 7

Calculate whether there has been a significant increase over the average 2010 figure of $18
reported in the neighborhood newspaper. State the hypotheses, alpha, df, and critical value.
Write a report including all necessary information about your results.

I surveyed each house on the block to determine how much we are spending on Halloween
treats. The distribution below represents the results in dollars.
$Spent f
50-59 1
40-49 2
30-39 5
20-29 12
10-19 7
0-9 7
Calculate the 90% confidence interval of the mean and present it in a sentence that shows
your understanding of the meaning of the confidence interval.

There are 6 cherries, 3 oranges and 2 lemon candies. What is the probability of getting 3 cherries ?