Math Answers

The mean number of births per minute in a country in a recent year was about nine. Find the probability that the

number of births in any given minute is (a) exactly six, (b) at least six, and (c) more than six.

The average number of miligrams (mg) of cholesterol in a cup of a certain brand of ice cream is 660 mg, the standard deviation is 35 mg. Assume the variable is normally distributed.

A. If a cup of ice cream is selected, what is the probability that the cholesterol content will be more than 670 mg?

B. If a sample of 10 cups of ice cream is selected, what is the probability that the mean of the sample will be larger that 670 mg?

a) A three digit number is to be formed using the digits 1, 2, 3, 4, 5, 6 and no repetition is

allowed.

i) How many numbers can be formed if the leading digit is 4?

ii) How many numbers can be formed if the number is more than 250?

iii) How many odd numbers can be formed between 200 and 400?

b) Consider a bookshelf contains 28 books in different genre. 14 books are in education, 9

books in business and 5 books in motivation. A student would like to take 15 books. Find the number of ways if:

i) there is no restriction

ii) the choice must consist of 8 books in education, 5 books in business and 2 books in

motivation genre.

iii) The choice must consist of at least 9 books in education and exactly 5 books in

motivation genre.

For the most recent year available, the mean annual cost to attend a private university in the United States was $26,889. Assume the distribution of annual cost follows the normal distribution and the standard deviation $4,500. 95% of all students at private university pay less than what amount?

1. A population consists of six values (6, 9, 12, 15, 18, and 21). (35 points) a. Select a random sample of size 3. Explain the random sampling that you used. (3 pts.) b. How many possible samples can be drawn? (3 pls.)

c. list all possible samples and compute the mean of each sample. (10 pls.)

d. Construct a frequency distribution of the sample means obtained in step 2 including

f: P(x): P(): *P(): EP(x): Ex-P(F) and 2 P(F). (13 pts.)

e. Determine the mean, voriance and standard deviation of the sample mean. (6 pts.)

Construct the Tabular Representation and Histogram Representation of the following probability distribution:

1. In a class of 100 students, 80 students passed in all subjects, 10 failed in one subject, 7 failed in two subjects and 3 failed in three subjects. Find the probability distribution of the variable for number of subjects a student from the given class has failed in.

2. The probability of landing on 1 is 0.25. The probability of landing on 2 is 0.75. Let X be the sum of the two spins. Construct a probability distribution for the random variable x.

For a certain type of fluorescent light in a large building, the cost per bulb of replacing bulbs all at once is much less than if they are replaced individually as they burn out. It is known that the lifetime of these bulbs is normally distributed, and that 60% last longer than 2500 hours, while 30% last longer than 3000 hours.

a) What are the approximate mean and standard deviation of the lifetimes of the bulbs?

If the light bulbs are completely replaced when more than 20% have burned out, what is the time between complete replacements

Say 40% of the class is female. What is the probability that 6 of the first 10 students walking in will be female?

Two functions f : R → R and g : R → R are defined by f(x) = 5x3 + 1 and g(x) = 2x − 3 for all x ∈ R.

Determine the inverse of (f -1 ◦ g) and (g ◦ f )(2) and ( f ◦ g)(2).