Statistics and Probability Answers

The average hourly wage of a sample of 150 workers in plant A was Rs. 2.56
with a standard deviation of Rs. 1.00. The average hourly wage of a sample of
200 workers in plant B was Rs. 2.87 with a standard deviation of Rs. 1.20.
Write a suitable hypothesis to test whether the wages are comparable
and test it.

White Blood Cell (WBC) count per cubic millimeter of whole blood has approximately the normal distribution with mean 7500 and standard deviation of 1750. The lowest 3% of all WBC counts are defined to probable risks. How low must one’s WBC count be to fall in the at-risk group?

The SAT reasoning test is perhaps the most widely used standardized test for college admissions in US. Scores follow a normal distribution with a mean of 1500 and a standard deviation of 300. Clinton College would like to offer an honors scholarship to students who score in the top of 5% of this list. What is the minimum score that qualified for the scholarship?

According to a government study among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $1,994. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $450.
a) What percent of the adults spend between $2,500 and $3,000 per year on reading and entertainment?
b) What percent spend less than $1,000 per year on reading and entertainment?

According to the South Dakoda Department of Health, the mean number of hours of TV viewing per week is higher among adult women than men. A recent study showed women spent an average of 34 hours per week watching TV and mean 29 hours per week. Assume that the distribution of hours watched follows the normal distribution for both groups, and that the standard deviation among the women is 4.5 hours and is 5.1 hours for the men.
a) How many hours of TV do the 5% of women who watch the most TV per week watch?
b) Find the comparable value for the men.

The SAT reasoning test is perhaps the most widely used standardized test for college admissions in US. Scores follow a normal distribution with a mean of 1500 and a standard deviation of 300. Clinton College would like to offer an honors scholarship to students who score in the top of 5% of this list. What is the minimum score that qualified for the scholarship?

In a study on survival time for ten patients following a new treatment for AIDS. The time in months were given thus: 24, 12, 8, 20, 3, 18, 24, 25,and 27.Determine the mode for the given data.

24. Rosalie Friend (2001), and educational psychologist, compared three methods of teaching writing. Students were randomly assigned to three different experimental conditions involving different methods of writing a summary. At the end of the two days of instructions, participants wrote a summary. One of the ways it was scored was the percentage of specific details of information it included from the original material. Here is a selection from her article describing one of the findings:

The effect of summarization method on inclusion of important information was significant F(2, 144) = 4.1032, p < .019. The mean scores (with standard deviations in parantheses) were as follows: Argument Repetition, 59.6% (17.9); Generalization, 59.8% (15.2); and Self-Reflection, 50.2% (18.0). (p.14)

Customers arrive at a single window server according to a Poisson distribution with mean 10
minutes, and the service time is exponential with mean 6 minutes per customer. Find the
following:
(i) expected number of customers in the system;
(ii) expected number of customers in the queue;
(iii) variance of the queue length

A company estimates that 0.2% of their products will fail after the original warranty period but within 2 years the purchase with a replacement cost of $350
IF they offer a 2 year extended warranty for $53 what is the company's expected value of each warranty sold?