Statistics and Probability Answers

Suppose X₁,X₂,...,X₂₅ is a random sample from P (λ = 320). Use the central limit theorem to approximate P(X̄ >542)

Scores on a test can be approximated with a normal distribution. If the average score was an 30 and the standard deviation was 4, find the probability that a randomly chosen test has a score of a) Below 40          b) between 30 and 35

Investment

A person may earn ₱100,000.00 by investing in the stocks of an international 

company with a probability of 0.40 or lose ₱35,000.00 over the same period 

with a probability of 0.60. Let X denote the net gain of a person who will invest 

in the company, construct the probability distribution of X, and compute for 

the expected value of a person who will invest in the same company. Interpret 

the result

We know that 10% people who purchase cars buy manual transmissions and 90% people purchase automatics.Three people purchase a car. find the probability distribution for the number who purchase automatics

We know that 10% people who purchase cars buy manual transmissions and 90% people purchase automatics.Three people purchase a car. find the probability distribution for the number who purchase automatics

The average pre-school cost for tuition fees last year was ₱17,250. The following tear, 20 institutions had a mean of ₱16,150 and a standard deviation of ₱2,250. Is there sufficient evidence at a = 0.10 level of significance to conclude that the mean cost has increased?

Five hundred children participated in a field demonstration. Their heights averaged is 110 cm with a standard deviation of 6 cm. What is the probability that the height of a child picked at random is less than 104cm?

The average precipitation for the first 7 months of the year is 19.32 inches with a standard deviation of 2.4 inches. Assume that the average precipitation is normally distributed. What is the probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months?

The weights of male students are normally distributed with a mean of 150 lbs. and a standard deviation of 25 lbs. What is the probability that 25 randomly selected make students will have a mean weight of more than 155 lbs?

A test taken by five people has a maximum score of 100. Their scores are 78, 65, 86, 91 and 68. 

1. Compute for the mean of the population.

2. Compute for the variance of the population.

3. List all the possible samples of size 3 that can be drawn from the population and compute for the mean of each sample. Use SRSWOR method.

4. Construct the probability distribution of the sample means.

5. Compute the mean of the sampling distribution of the sample means.

6. Compute the variance of the sampling distribution of the sample means