State Farm Insurance studies show that in Colorado, 50% of the auto insurance claims submitted for property damage were submitted by males under 25 years of age. Suppose 8 property damage claims involving automobiles are selected at random. (a) Let r be the number of claims made by males under age 25. Make a histogram for the r-distribution probabilities. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot Incorrect: Your answer is incorrect. (b) What is the probability that five or more claims are made by males under age 25? (Use 3 decimal places.) (c) What is the expected number of claims made by males under age 25? What is the standard deviation of the r-probability distribution? (Use 2 decimal places.) μ σ
In: Statistics and Probability
The Mountain States Office of State Farm Insurance Company reports that approximately 72% of all automobile damage liability claims were made by people under 25 years of age. A random sample of seven automobile insurance liability claims is under study. (a) Make a histogram showing the probability that r = 0 to 7 claims are made by people under 25 years of age. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot Correct: Your answer is correct. (b) Find the mean and standard deviation of this probability distribution. (Round your answers to two decimal places.) μ = claims σ = claims For samples of size 7, what is the expected number of claims made by people under 25 years of age? (Round your answer to the nearest whole number.) claims
In: Statistics and Probability
In a study on the physical activity of young adults, pediatric researchers measured overall physical activity as the total number of registered movements (counts) over a period of time and then computed the number of counts per minute (cpm) for each subject (International Journal of Obesity, Jan. 2007). The study revealed that the overall physical activity of obese young adults has a mean of 320 cpm and a standard deviation of 100 cpm. In a random sample of n = 100 obese young adults:
a) Describe the distribution of the average overall physical activity level of this sample obese young adults. What are the values of mean and standard deviation for this distribution?
b) What is the probability that the mean overall physical activity level of the sample is greater than 325 cpm?
c) What is the probability that the mean overall physical activity level of the sample is between 310 and 315 cpm?
In: Statistics and Probability
Scores for a common standardized college aptitude test are
normally distributed with a mean of 481 and a standard deviation of
108. Randomly selected men are given a Test Prepartion Course
before taking this test. Assume, for sake of argument, that the
test has no effect.
If 1 of the men is randomly selected, find the probability that his
score is at least 537.1.
P(X > 537.1) =
Enter your answer as a number accurate to 4 decimal places. NOTE:
Answers obtained using exact z-scores or z-scores
rounded to 3 decimal places are accepted.
If 12 of the men are randomly selected, find the probability that
their mean score is at least 537.1.
P(M > 537.1) =
Enter your answer as a number accurate to 4 decimal places. NOTE:
Answers obtained using exact z-scores or z-scores
rounded to 3 decimal places are accepted.
In: Statistics and Probability
Sarah Douds was rejected for employment from USA Credit Union. She then learned that USA Credit Union has hired only three women among the last 21 new employees. She then learned that there were a large number of applicants with an approximately equal number of qualified men as qualified women.
Help her address the charge of gender discrimination
by finding the probability of getting three or fewer women when 21
people are hired, assuming that there is no discrimination based on
gender.
(Report answer accurate to 8 decimal places).
P(at most three) =
Because this is a serious claim, we will use a stricter cutoff value for unusual events. We will use 0.5% as the cutoff value (1 in 200 chance of happening by chance). With this in mind, does the resulting probability really support such a charge?
yes, this supports a charge of gender discrimination
no, this does not support a charge of gender discrimination
In: Statistics and Probability
Scores for a common standardized college aptitude test are
normally distributed with a mean of 514 and a standard deviation of
97. Randomly selected men are given a Test Prepartion Course before
taking this test. Assume, for sake of argument, that the test has
no effect.
If 1 of the men is randomly selected, find the probability that his
score is at least 555.2.
P(X > 555.2) =
Enter your answer as a number accurate to 4 decimal places. NOTE:
Answers obtained using exact z-scores or z-scores
rounded to 3 decimal places are accepted.
If 16 of the men are randomly selected, find the probability that
their mean score is at least 555.2.
P(M > 555.2) =
Enter your answer as a number accurate to 4 decimal places. NOTE:
Answers obtained using exact z-scores or z-scores
rounded to 3 decimal places are accepted.
In: Statistics and Probability
The number of new cars sold by a company in a financial year can be approximated by a normal distribution with a mean of 125,000 cars and a standard deviation of 35,000 cars.
Answer: Click or tap here to enter text.
Answer: Click or tap here to enter text.
Answer: Click or tap here to enter text.
Answer: Click or tap here to enter text.
In: Statistics and Probability
A total of 8 neutrinos, presumably from Supernova 1987A, as observed in an underground detector located in a salt mine near Cleveland.
(a) If the average number of "background" neutrinos observed per day is know to be 2, calculate the probability that 8 or more such background events will be detected in one day.
(b) If the average number of "background" neutrinos observed per day is know to be 2, calculate the probability that 8 or more such background events will be detected in a 10-minute period.
(c) Based on your answers to parts (a) and (b): Should the experimenters (call them Team A) who observe 8 or more events distributed over a one-day period publish their results as a "discovery," or simply attribute these "events" to a fluctuation in the background rate? If Team B observes 8 or more events within a 10-minute period, is this an important discovery, or likely statistical fluctuation?
In: Statistics and Probability
At a certain coffee shop, all the customers buy a cup of coffee and some also buy a doughnut. The shop owner believes that the number of cups he sells each day is normally distributed with a mean of 330 cups and a standard deviation of 23 cups. He also believes that the number of doughnuts he sells each day is independent of the coffee sales and is normally distributed with a mean of 170 doughnuts and a standard deviation of 13. Complete parts a) through c).
Question: The shop is open every day but Sunday. Assuming day-to-day sales are independent, what's the probability he'll sell over 2000 cups of coffee in a week? _____________ (round to three decimals as needed.)
Question: Whats the probability that on any given day he'll sell a doughnut to more than half of his coffee customers ? ___________ (round to three decimal places as needed).
In: Math
In a study on the physical activity of young adults, pediatric researchers measured overall physical activity as the total number of registered movements (counts) over a period of time and then computed the number of counts per minute (cpm) for each subject (International Journal of Obesity, Jan. 2007). The study revealed that the overall physical activity of obese young adults has a mean of m = 320 cpm and a standard deviation of s = 100 cpm. (In comparison, the mean for young adults of normal weight is 540 cpm.) In a random sample of n = 100 obese young adults, consider the sample mean counts per minute, x.
a. Describe the sampling distribution of x.
b. What is the probability that the mean overall physical activity level of the sample is between 300 and 310 cpm?
c. What is the probability that the mean overall physical activity level of the sample is greater than 360 cpm?
In: Statistics and Probability