All work must be clearly shown for credit.
1. As of 5/5/22, Riverside County had 61.0% of eligible residents fully vaccinated. If six eligible residents are randomly selected from Riverside County, find the probability of each: (6 pts)
a) All six are vaccinated (x = 6).
b) None are vaccinated (x = 0).
c) At least one is vaccinated (x ≥ 1).
2. Mega Millions California lottery involves picking 5 numbers from 1 to 70. If you choose a 5-number combination, what’s the probability that it will be the winner? (4 pts)
3. The given probability distribution describes customer ratings for a vented range hood at Home Depot. Find:
a) Expected value (mean average)
b) Standard deviation (SD = sigma)
c) Low and High Normal limits (8 pts)
| Stars (x) | Ratings Pr(x) |
| 5 | 42% |
| 4 | 33% |
| 3 | 15% |
| 2 | 0% |
| 1 | 10% |
4. A company purchases machine components after randomly selecting 15 components and testing for defects. If the components have a 2.5% rate of defects, use the binomial distribution to find the probability of each: (12 pts)
a) Getting no defects (x = 0).
b) Getting 2 or fewer (x ≤ 2) defects.
c) Getting 3 or more (x ≥ 3) defects.
d) Getting at least one defect (x ≥ 1)
e) Find the mean and standard deviation.
f) Would it be a rare event to get 3 defects?
5. Find the probability Z ≤ 1.75 using the Standard Normal distribution (). (9 pts)
Pr (Z ≤ 1.75)
6. Suppose rainfall at Big Bear Lake dam has a normal distribution with mean average rainfall of 26 inches and standard deviation of 4.5 inches
. What’s the probability that a randomly selected year has between 18 and 32 inches of rainfall
? (9 pts)
7. Test scores had a mean of 100 points and standard deviation of 15
. If 16 students
are randomly selected, find the probability that their sample mean
score is greater than 110 points
. Assume test scores follow a normal distribution. (9 pts)
8. Suppose replacement times for washing machines are normally distributed with a mean of 10 years and a standard deviation of 2.5 years
. (9 pts)
a) Find the replacement time that separates the bottom 90% from the top 10%.
b) Find the replacement time that separates the bottom 25% from the top 75%
9. Find the 99% confidence interval (CI) and margin of error (ME) for systolic blood pressures for women aged 18-24 when: Interpret your results. (8 pts)
10. Find the 96% confidence interval (CI) and margin of error (ME) for the mean heights of men when: Interpret your results. (8 pts)
11. Find the 95% confidence interval (CI) and margin of error (ME) used to estimate the population proportion in a clinical trial with 124 subjects when 19.4% experienced nausea from the treatment. Interpret your results. (8 pts)
12. Find the minimum sample size needed () to estimate the mean monthly earnings of students at Norco college. We want 95% confidence that we are within a margin of error of $150 when the population standard deviation is known to be $625
. (5 pts)
13. Find the minimum sample size () you should use to be within a margin of error of 3.5% with a 90% confidence level when
and
are unknown. (5 pts)
