# Basic Statistics and Probability

Hi,

Would like some assistance with the following statistics problems in the attachment. Thanks.

1. The UAA Writing Institute finds that 30% of the general population in Alaska is left handed.

a. If 6 people are randomly selected, find the probability that between 3 and 5 are left handed.

b. If 6 people are randomly selected, find the probability that at least 4 of them are right handed.

c. If 6 people are randomly selected, find the probability that at most one of them are left handed.

d. If 6 people are randomly selected, find the probability that all are right handed.

2. Commander and Chief George W. Bush has been concerned with the number of helicopter crashes per week in Iraq. Over the last four years he noted that there were no helicopter crashes 35% of the time; there was one helicopter crash 27% of the time; there were two helicopter crashes 19% of the time; there were three helicopter crashes 11% of the time and there were four helicopter crashes 8% of the time. Based on the above information, assist President Bush in computing the mean, variance, and standard deviation of helicopter crashes in Iraq.

3. The chair of the Nursing Dept. at UAA hypothesizes that the final grades are distributed as 40% A's, 30% B's, 20% C's, 5% D's, and 5% F's. At the end of the current semester, the following grades were earned. At a 1% significance level, is the grade distribution for the Nursing Dept. different from what she expected.

GRADE A B C D F

NUMBER 45 52 39 8 6

4. An American roulette wheel contains 18 red numbers, 18 black numbers, and 2 green numbers. The following table shows the frequency with which the ball landed on each color in 200 trials.

COLOR Red Black Green

"O" Freq 88 102 10

At a 5% significance level do the data suggest that the roulette wheel is out of balance?

5. The city of Anchorage has three television stations, each with its own evening news program from 6:00 p.m. to 6:30 p.m. The Noonan Survey Group is hired to determine if there is a preference among the viewing audience for any station. A random sample of 150 viewers revealed that 53 watched the evening news on KENI-TV; 64 on KTUU-TV and 33 on KTVA-TV. At a 0.05 level of significance is there sufficient evidence to show that the three stations have equal shares of the evening news audience.

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#### Solution Preview

Please see the attachments.

1. The UAA Writing Institute finds that 30% of the general population in Alaska is left handed.

Answer

Let X be the number of left handed members in a sample of 6. Clearly X is binomial with n =6 and p =0.30. The probability density function of X is given by P(X=x)= . The P(X=x) for various values of x are given below

x P(X=x)

0 0.117649

1 0.302526

2 0.324135

3 0.18522

4 0.059535

5 0.010206

6 0.000729

a. If 6 people are randomly selected, find the probability that between 3 and 5 are left handed.

Here we need P(3≤X≤5)=0.185+0.0595+0.0102=0.254961

b. If 6 people are randomly selected, find the probability that at least 4 of them are right handed.

Here we need P(X≥4)=0.0595+0.0102+0.000729 =0.07047

c. If 6 people are randomly selected, find the probability that at most one of them are left handed.

Here we need P(X≤1)=P(X=0)+P(X=1)=0.420175

d. If 6 people are randomly selected, find the probability that all are right handed.

P(X=6)= 0.000729

2. Commander and Chief George W. Bush has been concerned with the number of helicopter crashes per week in Iraq. Over the last four years he noted that there were no helicopter crashes 35% of the time; there was one helicopter crash 27% of the time; there were two helicopter crashes 19% of the time; there were three helicopter crashes 11% of the time and there were four helicopter crashes 8% of the time. Based on the ...

#### Solution Summary

This solution gives the step by step method for computing probabilities based on Z score.