Statistics and Probability Answers

TRUE OR FALSE

1. In a probability distribution, the probability of each event in the sample space is greater than or equal to 1.

2. The number of tacos a food truck serves each day is an example of a discrete variable.

3. Surveying 25 people who just watched a movie to see if they liked the film is considered as a binomial experiment.

4. The total area under the normal distribution curve is less than 1.

5. The data values in a normal distribution curve is less on the area to the right of 4 standard deviations away on the right side of the
mean as compared to the area between 2 standard deviations from
the left and right side of the mean.

The number of hours outside of class that students spend per week on a business statistics course is approximately normally distributed with a mean of 6 hours and a standard deviation 3.2 hours. Suppose there are 300 students registered for this course, approximately how many students work for more than four hours per week?

Using the sample T-Test formula, work on the following problem.
Suppose the average GPA of college students who use memory enhancer is 1.75. You surveyed seven college students who do not use memory enhancers. Their GPAs are as follow: 1.65,1.78, 1.74, 1.6, 1.79, 1.81, and 1.85. Using the .05 alpha level, do students who use memory enhancers greatly differ from those who don't use memory enhancers in terms of GPA?

The new memory enhancer X recently gained a reputation in the market as the most effective memory enhancer ever produced by XY Pharma. The recorded average memory level among people who had taken the enhancer was 95 with a standard deviation of 10. As a neuroscientist, you want to test the claim and conducted a study and measure the memory level of 50 participants. The average memory level of the participants came out to be 80. Compute the effect size using the formula in the example above.

The lifetimes of the light bulbs produced by Filip Company are normally distributed with a mean of 1,150 hours and a standard deviation of 175 hours.
What is the probability that a randomly chosen light bulb will have a lifetime of more than 1,000 hours?

The lifetimes of the light bulbs produced by Filip Company are normally distributed with a mean of 1,150 hours and a standard deviation of 175 hours.

What is the probability that a randomly chosen light bulb will have a life time of more than 1000 hours?
What percentage of the light bulbs would be expected to last between 1000 and 1500?

The Poisson binomial distribution is the distribution of the sum of independent
Bernoulli random variables that are not necessarily identically distributed. In other words,
the success probability is different for each Bernoulli random variable. Suppose that we have
n Bernoulli trials where the i-th experiment is a success with probability pi. The number of
successes is X.
(a) Calculate the mean and variance of X.
(b) Suppose that n = 4. Calculate P(X = 2).

For the set of data below, determine the 5 number summaries. Construct the resulting box and whisker plot.
5, 3, 8, 6, 1, -10, 3, 9, 7, 4, 2,