Florida International University

Business Statistics - STA 2023

Ms. Laura Reisert Instructor

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REVIEW

1. TRUE/FALSE

__ If a events A and B are independent, they are also mutually exclusive.

__ In a normally distributed population approximately 68% of the measurements will lie within two standard deviations of the mean.

__ The mean of a binomial random variable is np.

__ The variance is the square root of the standard deviation.

__ The binomial and normal distributions are examples of discrete probability distributions.

__ The sample standard deviation is a measure of central tendency.

__ Fifty percent of the measurements in a data set will lie below the mean.

__ If P(AUB)=P(A)P(B), the events A and B are independent.

__ The population standard deviation is always a non-negative number.

__ The mean of a population is always a larger number than the standard deviation of that population.

2. The mean weight of American men is 170 pounds with a standard deviation 30 pounds. The weights are normally distributed.

a) If an American male is randomly selected, what is the probability that his weight exceeds 175 pounds?

b) If a sample of 50 American male is chosen, what is the probability their mean weight exceeds 175 pounds?

3. Consider the following sample: 2.6, 2.9, 3.1, 2.6, 1.4, 1.3. Find the

a) mean b) median c) mode d) range e) standard deviation

4. In a random sample of 100 voters, 62 were not registered Democrats. Give a 97% Confidence interval for the proportion of registered Democrats in the population.

5. The mean time to complete a task for a group of employees is 5.3 seconds with a standard deviation of 1.6 seconds. If a random sample of 60 employees is selected, what is the probability that the mean time for these employees to complete the task is less than five seconds?

6. Suppose 80% of the entering Freshmen at FIU attended high school in Miami-Dade County. In a random sample of 20 entering Freshmen at FIU, what is the probability that at least sixteen attended high school in Miami-Dade County?

7. Winter weather bureau records for the city of Buffalo indicate that it snows 28% of the days, is cloudy 52% of the days, and is snowy and cloudy 10% of the days. What is the probability a randomly selected winter day is ether snowy or cloudy?

8. Would you expect that following distribution to be symmetric, skewed right, or skewed left? Explain.

The ages of students in freshmen college course.

9. A battery manufacturer claims that its batteries have a mean life of at least 50 hours. In a sample of 100 batteries the mean life is found to be 45 hours with a standard deviation of 4 hours. Do you have enough evidence to dispute the manufacturer's claim with significance level of .02?

ANSWERS

1. F, F, T, F, F, F, F, F, T, F

2. a) .4325 b) .1190

3. a) 2.3 b) 2.6 c) 2.6 d) 1.8 e) .77

4. (.275, .485)

5. .0735

6. .630

7. .70

9. z = -12.5, yes