# Probability and Statistical Analysis

1. About 16% of the population of a large country is hopelessly romantic. If two people are randomly selected,

What is the probability both are hopelessly romantic?

What is the probability one person is hopelessly romantic?

Round to Four Decimal

2. Researchers conducted experiment with trees. Listed below are weights (kg) of tree given no fertilizer and trees with fertilizer and irrigation. Find the range, variance and standard deviation for each of the two samples, then compare the two sets of results. Does there appear to be a difference between the two standard deviations?

No Treatment: 0.22 0.28 0.12 0.04 0.28

Fertilizer and Irrigation: 1.05 0.38 1.79 0.68 1.91

Find the range for the trees that were given no treatment.

Range= ____ kg

Find the range for the trees treated with fertilizer and irrigation.

Range= ____ kg

Find the sample variance and sample standard deviation for the trees that were given no treatment.

Sample Variance= ____kg2 (Round to Three Decimal)

Sample Standard Deviation= ______ kg

3. During a quality assurance check, the actual coffee content (in ounces) of six jars of instant coffee was recorded as 6.03, 5.63, 6.40, 6.01, 5.98 and 6.02

A. Find the mean and the median of the coffee content

The mean coffee content is ________ounces. (Round Thee Decimal)

The median coffee content is ________ounces. (Round Thee Decimal)

B. The third value was incorrectly measured and is actually 6.04. Find the mean and median of the coffee content again

After correcting the data error, the mean coffee content is ____ounces. (Round Thee Decimal)

After correcting the data error, the median coffee content is ____ounces. (Round Thee Decimal)

C. Which measure of central tendency, the mean or the median, was affected more by the data entry error?

_____Mean _____Median

4. The mean for statistics test scores is 62 and the standard deviation is 6.0. For the biology test scores, the mean is 21 and the standard deviation is 3.9. The test scores of a student who took both tests are given below:

A student gets a 76 on the statistics test and a 27 on the biology test

A. Transform the statistics test score to a z-score

Z= _______ (Round to nearest hundredth)

Transform the biology test score to a z-score

Z= _______ (Round to nearest hundredth)

B. Determine on which test the student had a better score. Choose the correct answer below:

____ The scores on both tests are the same

____On the biology test the student had a better score

____On the statistics test the student had a better score

5. The table below shows the results of a survey that asked 2853 people whether they are involved in any type of charity work. A person is selected at random from the sample. Complete part (a) through (e):

Frequently Occasionally Not at All Total

Male 221 455 798 1474

Female 205 430 744 1379

Total 426 885 1542 2853

A. Find the probability that the person is frequently or occasionally involved in charity work.

P (being frequently involved or being occasionally involved) = ___ (Round nearest thousandth)

B. Find the probability that the person is female or not involved in charity work at all.

P (being female or not being involved) = ___ (Round nearest thousandth)

C. Find the probability that the person is male or frequently involved in charity work.

P (being male or being frequently involved) = ___ (Round nearest thousandth)