## Exercises forSampling Distributions & The Central Limit Theorem miscellaneous on-line topics for Finite Mathematics 2e

Index of On-Line Text
Text for This Topic
Everything for Finite Math

1. Compute the sampling distribution for two tosses of a fair coin; X = 1 for heads, and X = 0 for tails.

2. Compute the sampling distribution for two tosses of a fair die; X = 1 for an even number, and X = 0 for an odd number.

3. Compute the sampling distribution for two tosses of an unfair coin, where P(H) = 0.25 and P(T) = 0.75; X = 1 for heads, and X = 0 for tails.

4. Compute the sampling distribution for two tosses of a fair die, X = 1 for a 1 or 2 number, and X = 0 for any other number.

5. Consider the following probability ditribution.

 X 0 1 5 P(X=x) 1/3 1/3 1/3

(b) Find the sampling distribution of the sample mean for samples of size n = 2.     Answer
(c) Show that X- is an unbiased estimator for .     Answer

6. Consider the following probability ditribution.

 X -1 0 3 P(X=x) 1/4 1/4 1/2

(a) Find .
(b) Find the sampling distribution of the sample mean for samples of size n = 2.
(c) Show that X- is an unbiased estimator for .

7. Select the correct options to make the following sentence correct.

The Central Limit Theorem says that, if the population distribution has mean µ and standard deviation , then, for samples of size n, the sampling distribution of is with mean and standard deviation = /n. For the theorem to hold, the population distribution .

8. Select the correct options to make the following sentence correct.

A statistic S is an unbiased estimator of a population parameter P of a random variable X if the in its sampling distribution is the value of P.

9. According to a 1995 study, the mean family income in the US was \$38,000 with a standard deviation of 21,000. If a consulting agency surveys 49 families at random, what is the probability that it finds a mean family income of more than \$41,500?     Answer

10. According to coach Simon, the average height of male soccer players in the US is normally distributed with mean 1.79 m with a standard devation of 0.04 m.
(a) In a randomly selected soccer team of 11 players, what is the probability that the averge height of the players is less than 1.77 m?
(b) In view of the small sample size, must you make any additional assumptions to justify the answer? Explain