complete these stats problems:

35.The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 46 ounces and a standard deviation of 3 ounces.Use the Standard Deviation Rule, also known as the Empirical Rule.

Suggestion: sketch the distribution in order to answer these questions.

a) 95% of the widget weights lie between: 40 and 52

b) What percentage of the widget weights lie between 37 and 52 ounces? 97.35%

c) What percentage of the widget weights lie above 43 ? _______________%

36.The maintenance department at the main campus of a large state university receives daily requests to replace fluorescent light bulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 53 and a standard deviation of 11. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 53 and 86?

ans =

22. Suppose in a group of 26 people, there are 8 men and 18 women. You select 2 people, one after the other (without replacement).

What is the probability of choosing a man and a woman?

Give answer as decimal rounded to 4 decimal places

3. A lottery costs $3 to play. Each ticket has a 3% chance of winning $80.What is the expected value of a ticket?

5.A jar contains 3 pennies, 2 nickels and 5 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins.

Find the probability X = 10.

Find the probability X = 11

6.A jar contains 5 pennies, 5 nickels and 2 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins.

Find the probability X = 10.

Find the probability X = 11.

Find the expected value of X.

13. A pharmaceutical company receives large shipments of ibuprofen tablets and uses an acceptance sampling plan. This plan randomly selects and tests 26 tablets, then accepts the whole batch if there is at most one that doesn't meet the required specifications. What is the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 14% rate of defects?

(Report answer as a decimal value accurate to four decimal places.)

P(accept shipment) =

14.According to Masterfoods, the company that manufactures M&M's, 12% of peanut M&M's are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. You randomly select five peanut M&M's from an extra-large bag of the candies. (Round all probabilities below to four decimal places; i.e. your answer should look like 0.1234, not 0.1234444 or 12.34%.)

Compute the probability that exactly two of the five M&M's are brown.

Compute the probability that two or three of the five M&M's are brown.

Compute the probability that at most two of the five M&M's are brown.

Compute the probability that at least two of the five M&M's are brown.

15.A local county has an unemployment rate of 8%. A random sample of 20 employable people are picked at random from the county and are asked if they are employed. Round answers to 4 decimal places.

a) Find the probability that exactly 3 in the sample are unemployed.

b) Find the probability that fewer than 2 in the sample are unemployed.

c) Find the probability that there aremore than 1 in the sample who are unemployed.

d) Find the probability that there areat most 2 in the sample who are unemployed.

16. According to a study, 60 % of adult smokers started smoking before 21 years old. 12 smokers 21 years old or older are randomly selected, and the number of smokers who started smoking before 21 is recorded.

Include at least 6 decimal places in your answers.

1. The probability that at least 7 of them started smoking before 21 years of age is

2. The probability that at most 10 of them started smoking before 21 years of age is

3. The probability that exactly 7 of them started smoking before 21 years of age is

17.United Airlines' flights from Boston to Atlanta are on time 50 % of the time. Suppose 11 flights are randomly selected, and the number of on-time flights is recorded.

Round answers to 3 significant figures.

The probability that exactly 8 flights are on time is =

The probability that at most 6 flights are on time is =

The probability that at least 7 flights are on time is =

18.According to a recent survey, 80% of students say that they do not get enough sleep. Assume the survey meets the conditions of a binomial experiment. Round your answers to three decimal places

In a random survey of 30 students, find the probability that exactly 27 of them will say that they do not get enough sleep: 0.07853

In a random survey of 30 students, find the probability that more than 27 of them will say that they do not get enough sleep:

21. A large fast-food restaurant is having a promotional game where game pieces can be found on various products. Customers can win food or cash prizes. According to the company, the probability of winning a prize (large or small) with any eligible purchase is 0.143.

Consider your next 28 purchases that produce a game piece. Calculate the following:

This is a binomial distribution. Round your answers to at least 4 decimal places.

a) What is the probability that you win 4 prizes? .2109

b) What is the probability that you win more than 7 prizes?

c) What is the probability that you win 2 prizes or fewer?