STAT 200 - Elementary statistics Problems

STAT 200

Be sure to show all your work for problems requiring calculations in order to earn partial credit for an incorrect answer. If you choose to just submit answers rather than complete solutions, let me know which type of technology you used.

Please highlight your final answer.
1. (1 point) Determine which of the four levels of measurement:
Voltage measurements from my house                        ____________
 Book genre       ____________
 Outside temperature in winter in Silver Spring  ____________
 Restaurant ratings on scale of 0-4 stars   ____________

2. (1 point) Determine type of sampling:
¬I collected shoe sizes from my family   ____________
1003 adults were called after their phone numbers were
randomly generated by computer   ____________
 Police stopped every sixth driver for sobriety test  ____________
  U.S. D.O.C. collected data by randomly selecting 8
  Federal prisons and surveying every prisoner ____________
 
3. (2 points) I collected radon samples from basements in
my neighborhood and obtained the following:
Radon in cPi Frequency
2-5 2
6-9 2
10-13 6
14-17 15
 
Identify class width      ______________
Identify class midpoints     ______________________
Identify class boundaries     ______________________
Create histogram

4. (1 point) A simple random sample of pages of my dictionary was collected.  These are the number of words defined on each page. Find the mean, median, mode, and midrange.
51     63     36     43     34     62     73     39     53     79
There are 1459 pages. Estimate the total number of words in the dictionary. Is the estimate likely to be an accurate estimate of the total number of words in the English language?

5. (1 point) Environmental scientists measured CO2 emissions of a sample of cars in tons. Is the value of 9.3 unusual? Base your answers on the standard deviation, which must be included in your answer.
7.2     7.1     7.4     7.9     6.5     7.2     8.2     9.3

6. (2 points) A simple random sample of starting weekly salaries for college graduates was obtained. What is the 5-number summary? Construct a boxplot.

664    693    698    714    751    753    779    789    802    818    834    836
 
7. (1 point) What is the probability of selecting a person who has high blood pressure or being male?

Has High Blood Pressure  
 Yes No
Male 201 288
Female 126 224
 What is the probability of selecting a woman?

8. (1 point) If 2 out of 100 second graders are randomly selected, find the probability that they are both boys and like spring:

 Spring Summer Fall Winter
Boys 39 35 8 4
Girls 6 5 2 1

a) With replacement?
b) Without replacement?

9. (1 point) Human body temperatures have a mean of 98.200 F and a standard deviation of 0.620 F. Convert each of the following to a z-score and determine if it is usual or unusual.

a. 96.900 F
b. 96.980 F

10.  (1 point) My parents lived in Florida and wanted to know the probability of winning the Florida Fantasy 5 if they bought one ticket. They had to pick the five winning numbers from 1–36. Each randomly selected number is different and order doesn’t matter.
 
11.  (2 points) Groups of five babies are randomly selected. In each group, the random variable x is the number of babies with green eyes.

x P(x)
0 0.528
1 0.360
2 0.098
3 0.013
4 0.001
5 0+

Is this a probability table? If not, why not?  If it is, what is the mean and standard deviation?

12. (1 points) 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? Why or why not?

13.  (1 point) Find the critical value:
a. Z0.02
b. Z0.01
c. Z0.10

14. (2 points) Assume adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15.

Find the probability that a randomly selected adult has IQ < 115
Find the probability that a randomly selected adult has IQ > 70
Find P30, which is the IQ separating the bottom 30% from the top 70%
 
15. (2 points) Assume women’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 < 6.2 because they would fit all but a few women with a ring guard. What’s wrong with this reasoning

2.4.16
Here are weekly instructions times for school children in different countries: 23.8 hours(Japan) 26.9 hours (China) 22.2 hours (U.S) 24.6 hours (UK) 24.8 hours (France). What do these results suggest about education in USA?