Originally Posted by

**Seansgirl1** ** **

1. Suppose that in the 2004, 10 percent of the voters are still undecided. Find the probability that among 5 voters questioned, exactly 2 of them are undecided.

Mr F says: Pr(X = 2) where X ~ Binomial (n = 5, p = 0.1)

2.On each SAT math section there are 50 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the standard deviation for the number of correct answers.

Mr F says: X ~ Binomial (n = 50, p = 1/4) therefore Var(X) = np(1-p).

**3.**Doug leads bird-watching trips every morning in March. The number of cardinals seen has a Poisson distribution with a mean of 2.0. Find the probability that on a randomly selected trip, the number of cardinals seen is 2.

Mr F says: Substitute $\displaystyle {\color{red}\mu = 2.0}$ into the Poisson pmf and calculate Pr(X = 2).

4.The ACME Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0 degrees Celsius at the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some give readings below 0 degrees (denoted by negative numbers) and some give readings above 0 degrees (denoted by positive numbers). Assume that the mean reading is 0 degrees and the standard deviation of the readings is 1.00 degrees. Also assume that the frequency distribution of errors closely resembles the normal distribution. If 7% of the thermometers are rejected because they have readings that are too high, but all other thermometers are acceptable, find the temperature that separates the rejected thermometers from the others.

Mr F says: X ~ Normal $\displaystyle {\color{red} (\mu = 0, \sigma = 1)}$. Pr(X > x) = 0.07. Use inverse normal technique to get x.

5.IQ scores of UIU professors are normally distributed with a mean of 105 and a standard deviation of 21. In a random sample of 90, approximately how many Profs will have IQs between 84 and 133?

Mr F says: Let X be the random variable *IQ of UIU professors*. Use normal distribution to calculate p = Pr(84 < X < 133).

Let Y be the random variable number of professors with IQ between 84 and 133. Then Y ~ Binomial (n = 90, p = p). E(Y) = np.

6.A study of the amount of time it takes a mechanic to rebuild the transmission for a 1998 Acura Integra shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.1 hours.

Mr F says: Assume an infinite population of mechanics. Then $\displaystyle {\color{red}\bar{X}}$ ~ Normal $\displaystyle {\color{red}\left( \mu = 8.4, \sigma = \frac{1.8}{\sqrt{40}} \right)}$. Calculate $\displaystyle {\color{red}Pr(\bar{X} > 8.1)}$.

7.Find the probability that in 200 tosses of a pair fair dice, we will obtain at least 40 sevens. Assume that it is a normal distribution.

Mr F says: Let p be the probability of getting a seven in a single toss. Then the normal distribution has $\displaystyle {\color{red}\mu = 200 p}$ and variance $\displaystyle {\color{red}\sigma^2 = 200 p (1 - p)}$. Find Pr(X > 40).