MAT201 Statistics. Question 1 (3 points)
Compute the probability for a random variable X with µ=10 and σ=2. Calculate P(X<14).
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Question 2 (3 points)
Suppose X ~ N (200, 10). This says that x is a normally distributed random variable with mean μ = 200 and standard deviation σ = 10. Suppose x = 170, calculate the z score.
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Question 3 (3 points)
Suppose X has a normal distribution with mean 80 and standard deviation of 10. Between what values of x do 95% of the values lie?
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Question 4 (3 points)
Suppose X ~ N (10, 6). This says that x is a normally distributed random variable with mean μ = 10 and standard deviation σ = 6. Suppose x = 20, then x= 20 means that it is:
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Question 5 (3 points)
The final exam scores in a statistics class were normally distributed with a mean of 70 and a standard deviation of five. What is the probability that a student scored more than 65% and less than 75% on the exam?
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Question 6 (3 points)
To get admitted to top universities, the applicant’s SAT (Scholastic Aptitude Test) score must be on a very high side. In terms of concepts learned in MAT201, this means that:
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Question 7 (3 points)
If the z score=25, σ=2 and µ=50, what is x?
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Question 8 (3 points)
The distribution of heights of adult American women is approximately normal with a mean of 64 inches and standard deviation of 2 inches. What percent of women is taller than 68 inches?
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Question 9 (3 points)
The final exam scores in a statistics class were normally distributed with a mean of 70 and a standard deviation of five. What is the probability that a student scored more than 75% on the exam?
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Question 10 (3 points)
Compute the probability for a random variable X with µ=10 and σ=2. Calculate P(9 < X < 11).
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Answer the following problems showing your work and explaining (or analyzing) your results. Submit your work in a typed Microsoft Word document.
1. The final exam scores listed below are from one section of MATH 200. How many scores were within one standard deviation of the mean? How many scores were within two standard deviations of the mean?
99 34 86 57 73 85 91 93 46 96 88 79 68 85 89
2. The scores for math test #3 were normally distributed. If 15 students had a mean score of 74.8% and a standard deviation of 7.57, how many students scored above an 85%?
3. If you know the standard deviation, how do you find the variance?
4. To get the best deal on a stereo system, Louis called 8 out of 20 appliance stores in his neighborhood and asked for the cost of a specific model. Below is the sample data set of prices he collected:
$216 $135 $281 $189 $218 $193 $299 $235
Find the standard deviation.
5. The Company collected a sample of the salaries of its employees. There are 70 salary data points summarized in the frequency distribution below:
Salary  Number of Employees 
5,001–10,000  8 
10,001–15,000  12 
15,001–20,000  20 
20,001–25,000  17 
25,001–30,000  13 
a. Find the standard deviation.
b. Find the variance.
6. Calculate the mean and variance of the sample data set provided below. Show and explain your steps. Round to the nearest tenth.
14, 16, 7, 9, 11, 13, 8, 10
7. Create a frequency distribution table for the number of times a number was rolled on a die. (It may be helpful to print or write out all of the numbers so none are excluded.)
3, 5, 1, 6, 1, 2, 2, 6, 3, 4, 5, 1, 1, 3, 4, 2, 1, 6, 5, 3, 4, 2, 1, 3, 2, 4, 6, 5, 3, 1
8. Answer the following questions using the frequency distribution table you created in No. 7.
a. Which number(s) had the highest frequency?
b. How many times did a number of 4 or greater get thrown?
c. How many times was an odd number thrown?
d. How many times did a number greater than or equal to 2 and less than or equal to 5 get thrown?
9. The wait times (in seconds) for fast food service at two burger companies were recorded for quality assurance. Using the sample data below, find the following for each sample:
a. Range
b. Standard deviation
c. Variance
Lastly, compare the two sets of results.
Company  Wait times in seconds  
Big Burger Company  105  67  78  120  175  115  120  59 
The Cheesy Burger  133  124  200  79  101  147  118  125 
10. What does it mean if a graph is normally distributed? What percent of values fall within 1, 2, and 3, standard deviations from the mean?
oSs_1512828
57081
57075
5
6
False
57089
7
1
57076
8
8
57083
False
9
57078
10
oSs_1512836