Tutorial -9(19-20th March)
Ques1. Select all of the following that are correct descriptions of the t distribution.
a) There are more scores in the tails than in a normal distribution.
b) There are more scores in the center than in a normal distribution.
c) It is leptokurtic.
d) You use it when you do not know the population standard deviation.
e) A t distribution with 20 degrees of freedom has 95% of its distribution within 1.96 standard
deviations of its mean.
Ques2. A t distribution with which of the following degrees of freedom is the closest to a normal
distribution?
A) 0
B) 2
C) 12
D) 50
Ques3. Show that Gamma(1/2)= √ .
Ques4. Suppose you randomly select 7 women from a population of women, and 12 men from a
population of men. The table below shows the standard deviation in each sample and in each
population.
Population
Women
Men
Population standard Deviation
30
50
Sample standard Deviation
35
45
a) Compute f statistic.
b) Find the cumulative probability associated with each of the f statistics.
Ques5. Nationally 74% of college freshman continue as sophomores. A particular school has 486 out
of all 600 freshmen stay. Is this unusual?
Ques6. From past experience a professor knows that the test score of a student taking her final
examination is a random variable with a mean of 75 and standard deviation of 8. How many
students would have to take the examination to ensure, with probability at least .95 that the class
average would be at least 73?
Ques7. The lifetime of a special type of battery is a random variable with mean 40 hours and
standard deviation 20 hours. A battery is used until it fails, at which point it is replaced by a new one.
Assuming a stockpile of 25 such batteries the lifetimes of which are independent, approximate the
probability that over 1100 hours of use can be obtained.
Ques8. One thousand independent rolls of a fair die will be made. Let X be the number of sixes,
which will appear. Find the probability that 160 <= X <= 190.
Ques9. A random sample of size 25 is taken from a normal population having a mean of 80 and a
standard deviation of 5. A second random of size 36 is taken from a different population having a
mean of 75 and standard deviation of 3. Find the probability that the sample mean computed from
the 25 measurements will exceed the sample mean computed from the 36 measurements by at least
3.4 but less than 5.9.Assume the difference of the means to be measured to the nearest tenth.
Ques10. Assume the sample variances to be continuous measurements. Find the probability that a
random sample of 25 measurements from a normal distribution with variance 6, will have a sample
variance of .
a) Greater than 9.1
b) Between 3.462 and 10.745.