Category: Uncategorized

Which of the following uses set builder notation to denote the set of all real numbers less than \(-5\)?

The probability of buying a movie ticket with a popcorn coupon is 0.717. If you buy 21 movie tickets, what is the probability that exactly 11 of the tickets have popcorn coupons? Round your answer to 3 decimal places if necessary.  Explain your reasoning.

Porter’s points per basketball game are normally distributed with a standard deviation of 7 points. If Porter scores 50 points, and the z-score of this value is 4, then what is his mean points in a game? Explain your reasoning.

A nursing student is planning his schedule for next semester.  He needs to take three courses.  Chemistry must be in the schedule.  The math options are either precalculus or trigonometry.  The English options are either writing, poetry, or literature.  All of the possibilities for his schedule are shown in the tree diagram below. What is the probability that his English class is not literature?  Explain your reasoning.   Image Description Tree diagram with three layers.  The first tier has one option: chemistry.  The second tier has two options: precalculus or trigonometry.  The third tier has three options for each: writing, poetry, and literature.  The 6 possible schedules are (1) chemistry, precalculus, writing; (2) chemistry, precalculus, poetry; (3) chemistry, precalculus, literature; (4) chemistry, trigonometry, writing; (5) calculus, trigonometry, poetry; (6) calculus, trigonometry, literature.

The probability for taking a yoga class is 0.60, the probability for taking a strength training class is 0.20, and the probability of taking both classes is 0.14.  What is the probability of taking a yoga or strength training class? Explain your reasoning.

Caitlyn wanted to track the growth of various fruits in the garden, so she decided to label them. Apples were labeled with 1, 2, 3, 4, 5, 6 Lemons were labelled with 1, 2 Melons were labelled with 1, 2, 3 If a single fruit is picked at random, what is the probability that the fruit is a lemon or has an even number? Explain your reasoning.

There is a bag of 12 marbles. The marbles are labeled with the numbers one through twelve. If you pick 3 without replacement, how many different ways can the marbles be selected as first, second, and third? Explain your reasoning.

There is a bag of 15 marbles. The marbles are labeled with the numbers one through fifteen. If you pick 3 without replacement, how many different ways can the marbles be selected as first, second, and third? Explain your reasoning.

Two students, Hadea and Emily, want to find out who has the higher GPA when compared to each of their schools. Hadea has a GPA of 3.50, and her school has a mean GPA of 3.25 and a standard deviation of 0.4 Emily has a GPA of 3.75, and her school has a mean of 3.05 and a standard deviation of 0.3. Who has the higher GPA when compared to each of their schools, and why?  Explain your reasoning.

A random sample of houses in a major city has a sample mean of \(\overline{X}=1350\) square feet and a sample standard deviation of \(s=120\) square feet.  Use the Empirical Rule to determine the approximate percentage of house sizes that lie between 1110 square feet and 1350 square feet. Explain your reasoning.