The college loan debt for a 22 year old college graduate is approximately normally distributed with a mean college loan debt of
Project III *
Directions: Answer all questions. In those examples where it ask for a graph choose the most likely graph from the choices below. Round all final answers to two decimals. Submit ONLY ANSWER Sheet, NOT questions. (50 pts)
Selection of Choices for all graph questions are in Table 1. A Graph choice may be used more than once or not at all.
Table 1
Problem A Worth a total of (23 Pts)
The college loan debt for a 22 year old college graduate is approximately normally distributed with a mean college loan debt of
$88,645 and a standard deviation of $19,045.
(Questions 1-3 = one Pt each and Questions 4 – 13 = two Pts each)
1) Define the Population of people for all these questions (1-13).
2) What is the mean of this distribution?
3) What is the standard deviation for this distribution?
4) What is the probability of a 22 year old college graduate selected at random will have a college loan debt less than $50,000?
5) Choose a Graph from Table 1 page 1, that best displays the shaded area of interest for the previous question .
6) What is the Probability a 22 year old college graduate has a debt greater than $90,000?
7) Choose a Graph from Table 1 on page 1, that best displays the shaded area of interest for the previous question.
8) What is the Probability a 22 year old college graduate has a college loan debt between $75000 and $95000?
9) Choose a Graph from Table 1 above, that best displays
the shaded area of interest for the previous question .
10) Find the exact student debt score that separates the highest 25% debt scores from the remaining distribution.
11) Choose the Graph from Table 1 above that best displays the shaded area for the previous question.
12) If we are looking for the students with the lowest college loan debt would we look on the left or right side of the graph?
13) Would a positive or negative z score cut off the lowest 75% of the distribution?
Problem B Worth 17 pts)
The distribution of the ages of U.S. commercial aircraft is normally distributed and with a mean of 18.2 years and a standard deviation of 11.9 years. The FAA wants to take a closer look at the commercial aircraft, so it randomly selects 36 commercial planes. The FAA wants to answer questions as shown below by using the statistical information they can calculate from these 36 planes.
(Questions 14-16 = 1 Pt each and Questions 17 – 23 = two Pts each)
14) Define the Population for all these questions in this Problem B.
15) To calculate our statistics for our questions below; Should we use the:
a) Distribution of all individual U.S. Commercial aircraft or
b) Distribution of Samples Means (DSM)
16) What is the mean of this distribution we use in answering the questions below?
17) What is the value of the standard deviation for this distribution we must use to answer the questions below?
18) What is the percentile rank of the sample mean of 17.5 ?
19) Choose a Graph from Table 1 above, that best displays the shaded area of interest for the previous question.
20) Find the Probability that the mean age of a sample mean is at least 15 years.
21) Choose a Graph from Table 1 above, that best displays the shaded area of interest for the previous question.
22) The FAA decides to give a special test to those aircraft that are not too old or not too young. So they decide to choose the middle 20% of this distribution of mean ages of planes. What two mean ages of the planes will be used to find this middle 20%?
23) Choose a Graph from Table 1 above, that best displays the shaded area of interest for the previous question.
Problem C (10 points) (Questions #24 – 28 (2pts each))
A laboratory tested 71 chicken eggs and found that the mean amount of cholesterol was 230 milligrams with a
? = 10.4 millgram.
The measures of the amount of cholesterol in chicken eggs forms approximately a normal distribution.
Determine the answers for the following questions:
24) What is the population under study?
25) What is the value of the point estimate for this example?
26) Create a 95 % Confidence Interval for the cholesterol content.
27) Create a 99 % Confidence Interval for the cholesterol content.
28) Calculate the Margin of Error for the 95% Confidence Interval.
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