Statistics and Probability Answers

In a Science test, the mean score is 42 and the standard deviation is 5. Assuming the scores are normally distributed, what percent of the score is:

Less than 50?

If a population with size 3 has a standard deviation of 2.4, what is the standard deviation of the sampling distribution of its means? The sampling distribution has a sample size of 2 and all possible samples are drawn without replacements.

Tests made on the breaking strength of 10 pieces of a metal gave the following results: 578, 572, 570, 568, 572, 570, 570, 572, 598 and 584 kg. Test if the mean breaking strength of the wire can be assumed as 577 kg

4. The mean breaking strength of the cables supplied by a manufacturer is 1850 with a SD of 100. By a new technique in the manufacturing process, it is claimed that the breaking strength of the cable has increased. To test this claim, a sample of 50 cables is tested and it is found that the mean breaking strength is 1875. Can we support the claim at 1% LOS?

The annual rainfall in San Francisco is approximately normal with mean 22 inches and

standard deviation 7.9 inches. What is the probability that the rainfall in San Francisco

in the next year will be between 20 inches and 30 inches?

 If the random variable X takes the values 1, 2, 3 and 4 such that

P(X = 1) = 3P(X = 2) = P(X = 3) = 5P(X = 4), find the probability distribution and

cumulative distribution function of X.

What is the area of the tail region of the t-distribution with 12 degrees of freedom that falls below the t-value -2.179?

When do we add the two corresponding areas of the z-score?