Statistics and Probability Answers

Based on a study conducted on residents in the United States, we found their salaries follow the normally distribution with a mean of $48600, and a standard deviation of $14000.
a) If we randomly select 50 residents from the United States, approximately how many of them will have salaries above $70000?
b) If we randomly select 10 residents from the United States, what is the probability that their average salary is between $45000 to $50000?
c) Knowing Jackie’s salary is 17% below the third quartile, what is her actual salary?

A manufacturing company produces batteries, the quality control manager found the following facts. A battery is either good or bad. Based on the previous record, the probability of selecting a bad battery is 0.04. The probability of producing each battery is independent of others.
a) If we randomly select 10 batteries, what is the probability that exactly 7 of them are good.
b) If we randomly select 15 batteries, what is the probability that at least 13 of them are bad.
c) If we randomly select 20 batteries, what is the probability that at most 18 of them are good.

Based on a sample of 178 residents in the United States, we found 95 of them support Joe Biden for the presidential election of 2020.
a) Suppose a statistician wants to construct a confidence interval for the proportion of all residents in the United States who support Joe Biden for the presidential election of 2020, what are the preliminary conditions that need to be verified, and what can we assume once the conditions are satisfied?
b) Construct a 88% confidence interval for the proportion of all residents in the United States who support Joe Biden for the presidential election of 2020, and state the confidence statement

A paint manufacturer uses a machine to fill gallon cans with paint. The manufacturer wants to estimate the mean volume of paint of the machine is putting in the cans within 0.3 ounce. Determine the minimum sample size required to construct a 89% confidence interval for the population mean. Assume the population standard deviation is 0.8 ounce.

The following table represents a sample of 500 people and their opinion on Tax Reform. Do we have enough evidence to conclude that Party Affiliation and Opinion on Tax Reform are dependent on 5% level of significance.

Affiliation/Opinion on Tax | Reforms | Favor | Indifferent | Opposed
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Democrat
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Republican

Assuming the lasting time of laptop batteries are normally distributed with a mean of 11 hours and a standard deviation of ) 0.7 hours.
a) If we randomly select 8 batteries, what is the probability that the average lasting time of these laptops is longer than 11.5 hours.
b) In a group of 30 laptops, approximately how many of them will last less than 10 hours?
c) Knowing that a lasting time of a laptop is 20% below the third quartile, how many hours can this laptop last?

The following probability model gives the probability structure of a lottery ticket sold in Florida.
X -$10 $1 $3 $10 $20
P(X) 0.5 0.25 0.15 0.09 0.01


Calculate the mean, variance, and standard deviation.

The following frequency table represents the weight of a random sample of 50 students where the largest value is 112 and the smallest value is 44.
a) Find the range and class width.
b) Complete the first 2 rows of the following table.
Class Limit | Class Boundaries | Midpoint | Frequency | Cumulative Frequency | Relative
Frequency
5
6

The following probability model gives the probability structure of a lottery ticket sold in Florida.
X -$10 $1 $3 $10 $20
P(X) 0.5 0.25 0.15 0.09 0.01


Calculate the mean, variance, and standard deviation.

A manufacturing company produces computer chips, the quality control manager found the following facts.
1. A chip is either good or bad.
2. Based on the previous record, the probability of selecting a good chip is 0.92.
3. The probability of producing each chip is independent of others.

a) If we randomly select 10 chips, what is the probability that exactly 8 of them are good.
b) If we randomly select 15 chips, what is the probability that no more than 2 of them are bad.
c) If we randomly select 20 chips, what is the probability that at least 18 of them are good.