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In the mid-1990s, time magazine reported that 27% of the US Congress supported a tax cut as a means of stimulating the economy and increasing Tax revenues. Suppose at that time five members of congress were randomly selected for an interview and asked whether they supported the tax cut to stimulate the economy.
Find the probability that:
2.1 At least three of the five members were in favour of a tax cut. (6)
2.2 Less than five members were in favour of a tax cut. (6)
2.3 Not more than 3 members were in favour of the tax. (6)
2.4 Find the mean of the above distribution (6)
2.5 Find the variance and standard deviation of the above distribution (6)
what is the probability that at least five out of 20 young executives practice good reading habits
The following data are the measures of the diameters of 36 rivet heads in 1/100 of an inch.
6.72 6.77 6.82 6.70 6.78 6.70 6.62 6.75
6.66 6.66 6.64 6.76 6.73 6.80 6.72 6.76
6.76 6.68 6.66 6.62 6.72 6.76 6.70 6.78
6.76 6.67 6.70 6.72 6.74 6.81 6.79 6.78
6.66 6.76 6.76 6.72
Compute the Arithmetic Mean, variance, standard deviation, Coe cient of Variation, Coe -
cient of Skewness and Coe cient of Kurtosis..
The weights of students in a certain school are normally distributed with a mean weight of 66 kg. 10% have a weight greater than 70kg. What percentage of students weighs between 62kg and 66kg?
Explicate a null hypothesis and its alternative hypothesis in (a) words and in (b) symbols for each of the following. Tell whether the test is directional and non-directional.
1. A librarian of a school claims that all their senior high school students read an average of 10 books a month. A random sample of senior high students read an average 12 books. The confidence statement is 95%.
2. According to a factory employer, the mean working time of workers in the factory is 6. A researcher interviewed 50% of the employees and found out that their mean working time is 8 hours. The 𝛼 level is 0.05.
3. A random sample of 200 students got a mean score of 62 in a knowledge test in mathematics. In the standardization of the test, 𝜇=50.
A random sample of 11 observations was taken from normal population. The sample mean and standard deviation are 74.5 and 9 accordingly. Can we infer at 5% significance level that the population mean is greater than 70?
A random of 25 observations was drawn from a normal population. The sample mean and the sample standard deviation are 52 and 15 accordingly. Is there enough evidence at 10% significance level to infer that the population mean is not equal to 50? Estimate the population mean as well.
A secretary makes 2 errors per page on the average. What is the probability that on the next page she makes
a) 4 or more errors?
b) No errors?
The probability that a freshman entering AAU (Science Faculty) will survive first semester is 0.92. (From
1993/94 academic year statistics). Assuming this pattern remain unchanged over the subsequent years, what
is the probability that among 100 randomly selected freshmen in first semester,
a) None will survive?
b) Exactly 97 will survive?
c) At least three will survive?
Two dice are rolled. Let X be a random variable denoting the sum of the numbers
on the two dice.
i) Give the probability distribution of X
ii) Compute the expected value of X and its variance
