Statistics and Probability Answers

For a mean of 75 and a standard deviation of 3, find P(X ≥ 77 )

For a mean of 20 and standard deviation of 5, find P(X ≤ 17 )

Find the percentile for x=8 if the mean is 7 and the standard deviation is 2

Find the z-score for x=8 if the mean is 7 and the standard deviation is 2

The mean life of a tire is 30,000 km. The standard deviation is 2000 km.

a. 68% of all tires will have a life between ______ km and _____ km
b. 95% of all tires will have a life between ______ km and ______ km
c. What percent of the tires will have a life that exceeds 26,000 km ?
d. If a company purchased 2000 tires , how many tires would you expect to last more than 28,000 km ?

Which will have a continuous probability distribution

a. The length of a cut piece of wood
b. The number of marbles in bag
c. The number of children in a family
d. The mass of fish caught

Q1. Obtain the probability distribution of the number of aces in simultaneous throw of two unbiased dice.

Q2. Machine produces an average of 20% defective bolts. A batch is accepted if a sample of 5 bolts taken from that batch contains no defective and rejected it the sample contains 3 or more defectives. In other cases, a second sample is taken. What is the probability that the second sample is required ?

A sample of size 3 is to be selected from a population of 10 households. List all the
possible samples by:
i) Linear Systematic Sampling
ii) Circular Systematic Sampling

Also compare the two

Considering 6 cards fr a pack of cards without replacement . What is the probability that 3 of the cards will be black?

Assume that the total score (from both teams) for college football games averages μ = 42 points per game, and that the distribution of total points is approximately normal with σ = 20.
a. What is the probability that a randomly selected game would have more than 60 points?
b. What proportion of college football games have a point total between 20 and 60?