Statistics and Probability Answers

a company has made available to his employees (without charges) extensive club facilities that may be used before work, during the lunch hour, after work and on weekend. the record for the last year indicates that of 250 employees, 110 used the facilities at sometimes. of 170males employed by a company ,65 used the facilities, what is the probability that an employer chooses at random (setup contingency table)
a) is a female or has used the health club facilities
b) is a male and has not used the health club facilities c) suppose that we select the female employees of the company.what then the probability that she has used the health club facilities.

A dart hits the square dartboard shown below at a random point. Find the probability that the dart lands in the shaded circular region. Each side of the dartboard is
12in
, and the radius of the shaded region is
5in
.

Question 1)
Let X be a discrete random variable with probability math function defined by:

If x is a normal variable with the mean u=5 and variance (sigma square)=16, what is the probability that x is less than or equal to 6?

a tree farm owner measure 27 trees in his garden centre. mean diamter of 10.4 inches and standard dev of 4.7 inches.
Draw normal model for tree farm
What size would you expect the central 95% of trees to be?(Diagram required)
What percent of trees should be less than an inch in diameter?(diagram required)
What percent of trees should be between 4.9 and 10.4 inches.(diagram required)

An insurance company collects data on​ seat-belt use among drivers in a country. Of 1400 drivers 30-39 years​ old, 18​% said that they buckle​ up, whereas 379 of 1100 drivers 55-64 years old said that they did. Find a 98​% confidence interval for the difference between the proportions of​ seat-belt users for drivers in the age groups 30-39 years and 55-64 years.
Construct a 98​% confidence interval.
The 98​% confidence interval for P1−P2 is from _ to _

A publishing company has just published a new college textbook. Before the company decides the price at which to sell this textbook, it wants to know the average price of all such textbooks in the market. The research department at the company took a sample of 25 comparable textbooks and collected information on their prices. This information produced a mean price of $145 for this sample. It is known that the standard deviation of the prices of all such textbooks is $35 and the population of such prices is normal.

What is the point estimate of the mean price of all such college textbooks?
(b) Construct a 90% confidence interval for the mean price of all such college textbooks

The random variables X and Y have a density of
fXY (x, y) = x + y for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1, and fXY (x, y) = 0 elsewhere. Evaluate
E [X] and E [XY ].

A100 page book is known to have 200 printing errors distributed randomly through the pages.The probability that one of the page will be found to be completely free of errors is?

Let T be a random variable giving the number of heads in three tosses of a coin.list the elements of the sample space S for the three tosses of the coin and assign a value to each sample point.