Statistics and Probability Answers

It is estimated that 4000 of the 10,000 voting
residents of a town are against a new sales tax. If 15
eligible voters are selected at random and asked their
opinion, what is the probability that at most 7 favor
the new tax?

Among 150 IRS employees in a large city, only
30 are women. If 10 of the employees are chosen at
random to provide free tax assistance for the residents
of this city, use the binomial approximation to the hypergeometric
distribution to find the probability that
at least 3 women are selected.

A manufacturing company uses an acceptance
scheme on items from a production line before they
are shipped. The plan is a two-stage one. Boxes of 25
items are readied for shipment, and a sample of 3 items
is tested for defectives. If any defectives are found, the
entire box is sent back for 100% screening. If no defectives
are found, the box is shipped.

(a) What is the probability that a box containing 3
defectives will be shipped?

(b) What is the probability that a box containing only
1 defective will be sent back for screening?

What is the probability that a waitress will
refuse to serve alcoholic beverages to only 2 minors
if she randomly checks the IDs of 5 among 9 students,
4 of whom are minors?

a process yields 10% defective items. if 100 items are randomly selected from the process, what is the probability that the number of defectives

(a) exceeds 13?

(b) is less than 8?

1. Two students A and B can solve 50% and 80% problems are respectively from the exercise. What is the probability that either A or B can solve a problem chosen at random.
2. For any events A and B, it is known that P(A) = 2/3 P( A U B )= 7/12 and P (A ∩ B) = 5/12. Find P ( B ).

A random sample of size n1= 40 households in the first community has a mean monthly icome of 1900$ with a standard deviation 540$. For the second community a sample of n1= 30 households has a mean of 1600$ with a standard deviation 420$.Using a 5% level of significance, test the null hypothesis that there is no difference between the average monthly household income in the two communities.

Let X represent the weight in pounds of king salmon caught at the mouth of certain river and assume that X possesses a normal distribution with mean 30 and standard deviation 6. Calculate the probability that if a fisherman catches a salmon its weight will be:

a) At least 41 pounds
b) Between 20 and 40 pounds

. Suppose that Peter visits the hostel mess sometime between 12:00 noon and 2:00 p.m.. He leaves the
mess after finishing his lunch in 20 minutes. Likewise, Gwen visits the same hostel mess sometime
between 1:00 p.m. and 2:00 p.m.. She also leaves the mess after finishing her lunch in 20 minutes. If the
probability of arrival of each person is uniform across the given intervals respectively, find the probability
that they meet in the mess.

An overseas shipment of 5 foreign automobiles contains 2 that have slight
paint blemishes. If an agency receives 3 of these automobiles at random,
find the probability distribution of the random variable X representing the
number of automobiles with paint blemishes purchased by the agency.
Find the mean number of automobiles with paint blemishes.
Also calculate the variation