Question

1. Decide (write yes or no) whether the experiments are binomial experiments or not. Explain why or why not using a complete sentence:

a) You spin a number wheel that has 20 numbers 500 times. The random variable represents the number that is spun.

b) Surveying 300 prisoners to see whether or not they are serving time for their first offense. The random variable represents the number of prisoners serving time for their first offense.  Assume each prisoners response is independent.

2.Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children.

a. Find the probability of exactly 8 boys in 10 births. Round your answer to four decimal places.

b. What kind of distribution is this? How do you know?

3. Assume that the salaries of elementary school teachers in the U.S. are normally distributed with a mean of $32,000 and a standard deviation of $3000.

a. Using the Empirical Rule, we could estimate that about 95% of the elementary school teacher salaries are between what two values?

Answer 1

#1.
a) Not Binomial
Reason: Because the outcome of spinning the wheel will result into 20 different outcomes. Binomial experiment has two outcomes only.

b) Binomial
Here the outcome of prisoner's response will be either first time prisoner or not.

#2.
As per binomial distribution,
P(X=r) = nCr * p^r * (1-p)^(n-r)

a)
P(X = 8) = 10C8 * 0.5^8 * 0.5^2
P(X = 8) = 0.0439

b)
This is binomial distribution
Because there are only two possible outcomes, either male or female

#3.

As per Empirical Rule, 95% of the data will fall within two standard deviations of the mean.

Hence, 32000 - 2*3000 = 26000

and 32000 + 2*3000 = 38000

Hence two values are 26000 and 38000