Statistics and Probability Answers

A company produces mobile phones of which 3% are defective.
a) If 20 mobile phones are selected for testing, what is the probability that exactly 8 are defective?
b) If 12 mobile phones are selected for testing, what is the probability that more than 2 are not defective?
c) If a distributor gets a shipment of 1000 mobile phones, how many of these mobile phones do we expect to be defective, and what is the standard deviation?

Based on information from the Denver Post, it has been determined that the police response time of 5000 emergency calls have a mean of 8.4 minutes and a standard deviation of 1.7 minutes.
a) If we assume the data follows the normal distribution, for a randomly received emergency call, what is the probability that the response will be above 13.5 minutes?
b) If we assume the data follows normal distribution, approximately how many emergency calls are responded within 5 minutes?
c) If we assume the data follows a left skewed distribution, at least 68% of the emergency calls should have their response time between what range?
d) If we assume the data follows the normal distribution, for a randomly received emergency call, what is the probability that the response time will be between 6.7 to 11.8 minutes?
e) If we assume the data follow a right skewed distribution, for a randomly received emergency call, what is the probability that the response time will be between 5.34 to 11.46 minutes?

Assuming the life expectancy of horses follows the normal distribution with a mean of 27 years and a standard deviation of 1.2 years.
a) If we randomly select 13 horses, what is the probability that the average lifetime of the horses is greater than or equal to 28 years?
b) In a group of 35 horses, approximately how many of them will live between 25 to 30 years?
c) Knowing that a horse died earlier than 63% of all horses, approximately how many years does this horse live?

A survey found that 68% of adults ages 18 to 25 thunk that their generation is unique and distinct.
a) If we randomly select 12 adult ages 18 to 25, what is the probability that exactly 4 of them think their generation is not unique and distinct?
b) If we randomly select 16 adults ages 18 to 25, what is the probability that more than 14 of them think their generation is unique and distinct?
c) If we randomly select 20 adults ages 18 to 25, what is the probability that at least 2 of them think their generation is not unique and distinct?

A statistician studies the average age of professors in a local college in Georgia.
a) Based on a random sample of 25 professors, we found the average age is 54, with standard deviation of 6.3. Construct a 98% confidence interval for the population’s average age.
b) Based on another random sample of size 32, we found the average age is 53, assuming standard deviation of all professors in this college is 4.9. Construct an 83% confidence interval for the population’s average age and state the confidence statement.

According to a recent survey conducted at a local college, we found students spend an average of 19.5 hours on their smartphone per week, with a standard deviation of 3.5 hours. Assuming the data follows the normal distribution
a) How many percent of students in this college spend more than 15 hours on their smartphones per week?
b) If we randomly select 12 students, what is the probability that the average of these students spending on their smartphone is more than 20 hours per week?
c) What is the 36th percentile for number of hours spent on their smartphone per week?

Based on a study conducted on 10,000 houses in a countryside area, a realtor found the houses in this area is normally distributed with a mean of 2100 square feet, and a standard deviation of 600 square feet.
a) If we randomly select 6 houses, what is the probability that the average of these houses is above 2000 square feet?
b) Approximately how many houses are above 1500 square feet?
c) A house is selected at random, what is the probability that it is between 1700 to 2800 square feet?
d) Knowing a house is exactly 10% above the first quartile, what is its size?

If we examine the histogram, and found the size of these houses actually follows a left skewed distribution. Use this information to answer e) and f).
e) At least how many percent of the houses in this area are between 1320 to 2880 square feet.
f) At least 7700 houses in this area are between what ranges in square feet.

According to 32 randomly selected customers at a Burger King restaurant, we found the service time for the drive-through has a mean of 181.3 sec with a standard deviation of 82.2 sec. According to another 45 randomly selected customers at a McDonald’s restaurant in the same area, we found the service time for the drive-through has a mean of 167.8sec with a standard deviation of 60.6sec.
a) Test if the average service time at McDonald’s is less than Burger King at 2% level of significance. (Use both critical value method and p-value method)
b) According to the result that you have in part a), which type of error could you possibly make? Describe such error with the context of the problem.

Based on a survey of 150 AUS students, we found 36 of them do not eat breakfast. Describe the sampling distribution of the sample proportion, and find the point estimate and standard error.
a) Construct an 89% confidence interval of the percentage of all AUS students who eat breakfast and state the confidence statement.
b) Do we have enough evidence to conclude that less than 25% of AUS students do not eat breakfast at 9% level of significance? (Use both critical value method and p-value method)

Based on a survey of 130 AUS students, we found 36 of them are using iPhone. Do we have enough evidence to conclude that about 30% of AUS students are using iPhone at 15% level of significance?