Statistics and Probability Answers

Play the following games in the Games Fair:

• Three Prize Roller
• Word Scramble
• Marble Draw
• Ten Spinner

For each Games Fair game, answer the following questions:

1. Create the probability distribution in a table for all the outcomes where X is the random variable representing the number of points awarded.
2. Communicate how you arrived at the probability of each outcome.
3. What is the expected value, E(X), for the game? You may include this in your table from the distribution. If the game costs 10 points to play, how much would the player expect to win or lose?
4. Create the bar graph for the Probability Distribution.

Submit your work in one document created in a word processing program and spreadsheet. Take a screen capture of your charts and graphs and put them into the document. If you need to write math by hand to communicate how you arrived at your probabilities, you may take a picture of your work and insert it into the document. Save the document as a .pdf and submit it to your teacher.

When purchasing bulk orders of​ batteries, a toy manufacturer uses this acceptance sampling​ plan: Randomly select and test 41 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 3 batteries do not meet specifications. A shipment contains 4000 ​batteries, and 2​% of them do not meet specifications. What is the probability that this whole shipment will be​ accepted? Will almost all such shipments be​ accepted, or will many be​ rejected?

A bottler of drinking water fills plastic bottles with a mean volume of 1,000 milliliters (mL) and standard deviation of 7. The fill volumes are normally distributed. What is the probability that a bottle has a volume between 996ml and 1,002ml?

Over the last 3 years, Art's Supermarket has observed the following distribution of modes of payment in the express lines: cash (C) 41%, check (CK) 24%, credit or debit card (D) 26%, and other (N) 9%. In an effort to make express checkout more efficient, Art's has just begun offering a 1% discount for cash payment in the express checkout line. The following table lists the frequency distribution of the modes of payment for a sample of 500 express-line customers after the discount went into effect. Mode of payment CK Number of customers 240 104 111 45 Test at the 1% significance level whether the distribution of modes of payment in the express checkout line changed after the discount went into effect. Show the work for both classical approach and p-value approach. Make sure to show the work for the four steps diecused

The average salary of a male full professor at a public four-year institution offering classes at the doctoral level is $97,750. For a female full professor at the same kind of institution, the salary is $90,280. If the standard deviation for the salaries of both genders is approximately $4700 and the salaries are normally distributed, find the 80th percentile salary for the male professors and for female professors, respectively.

In a town 10 accidents took place in a period of 50 days. Assume that the number of accidents per day follow Poisson distribution. Find the probability that there will be three or more accidents per day.

Use the Desmos kept grabbing calculator to generate the least squares regression line and statistics for the data in the table. What is the residual value for X =18

X Y

2 3

4 9

11 12

15 17

18 16

25 22

Answers:

-0.4216

-1.2389

0.4216

2.5784

A computer center has three printers A, B and C, which print at different speeds. Programmes are routed to the first available printer. The probability that the programmes are routed to the first available printer. The probability that the programmes are routed to the printers A, B and C are 0.6, 0.3 and 0.1 respectively. Occasionally, a printer will jam and destroy a printout. The probability that printers A, B and C will jam are 0.01, 0.05 and 0.04 respectively. Your programme is destroyed when a printer jams. What is the probability that printer A is involved?

1. Blood glucose levels for obese patients have a mean of 100 with a <span style="font-size: 12pt; color: rgb(0, 0, 0); background-color: transparent; font-variant-numeric: normal; font-variant-east-asian: normal; vertical-align: baseline; white-space: pre-wrap;">standard deviation</span> of 15. A researcher thinks that a diet high in raw cornstarch will have a positive or negative effect on blood glucose levels. A sample of 30 patients who have tried the raw cornstarch diet have a mean glucose level of 140.
   

1. In a plant nursery, the owner thinks that the length of seedlings in a box sprayed with a new kind of fertilizer has an average height of 26cm after. One researcher randomly selected 18 such seedlings and calculated the mean  height to be 20cm and the standard deviation was 10cm.  Proceed with the test using ∞ = 0.05