Statistics and Probability Answers

A sales man knows that, on each visit to a customer, the probability of a sale is one fifth. Each day he makes three independent visits to customers.
Calculate the probability that, on a randomly selected day:
(a) all three visits result in sales. (5 marks)
(b) exactly two visits results in sales. (5 marks)
(c) less than two visits results in sales

The probability distribution of X, the number of imperfections per 10 meters of a synthetic fabric in continous rolls of uniform width, is given by:

x: 0 1 2 3 4
f(x): 0.41 0.37 0.16 0.05 0.01

Construct the cumulative distribution of X.

Find a formula for the probability distribution of the random variable X representing the outcome when a single die is rolled once.

Isabella rolled a numbered cube 300 times. How many times will Isabella expect to roll an even number?

A car manufacturer takes an average of 17.5 hours to construct a car. This includes time for stamping, welding, painting, assembly and inspections. Construction times vary with a standard deviation of 30 minutes and these times follow a normal distribution.
a. Find the construction time of a car, which is on the 10th percentile of this distribution.
b. What is the probability that a randomly selected car manufactured at this plant takes between 18 and 19 hours to construct?
c. Find the probability that the construction time for a randomly selected car manufactured at this plant is less than 17 hours and 50 minutes.

Suppose that the life of a certain type of electron tube has an exponential distribution with a mean life of 500 hours. Find the probability that it will last for another 600 hours if the tube has been in operation for 300 hours.

Let W be a random variable giving the number of heads minus the number of tails in three tosses of a coin. List the element of the sample space S for the three tosses of the coin and to each sample point assign a value of W.

A car manufacturer takes an average of 17.5 hours to construct a car. This includes time for stamping, welding, painting, assembly and inspections. Construction times vary with a standard deviation of 30 minutes and these times follow a normal distribution. Show your working, including an appropriate diagram. (You can simply paste a photo of the diagram into your solution).
Question: What is the probability that a randomly selected car manufactured at this plant takes between 18 and 19 hours to construct?

In an effort to estimate the annual income for new graduates, data were collected from 100 new graduates over a 1-year period. Assume a population standard deviation of $2,000.

If the sample mean is $15,000, what is the 95% confidence interval for the population mean?
Select one:
a. $14,608 to $15,392
b. $14,668 to $15,332
c. $14,590 to $15,410
d. $14,534 to $15,466
e. $14,603 to $15,396
Question 9
If the sample mean is $15,000, what is the 98% confidence interval for the population mean?
Select one:
a. $14,590 to $15,410
b. $14,608 to $15,392
c. $14,603 to $15,396
d. $14,668 to $15,332
e. $14,534 to $15,466

Test H0: m £ 8 versus HA: m > 8, given a = 0.01, n = 25, =8.13 and s = 0.25. Assume the sample is selected from a normally distributed population.