Assume that adults have IQ scores that are normally distributed with a mean of 95.9 and a standard deviation of 16.4. Find the following probabilities. Round your answers to three decimal places; add trailing zeros as needed.
The probability that a randomly selected adult has an IQ greater than 122.6 is .
The probability that a randomly selected adult has an IQ lower than 92.0 is .
The probability that a randomly selected adult has an IQ between 80.0 and 110.0 is .
In: Statistics and Probability
According to a study, the median time a patient waits to see a doctor in an emergency room is 30 minutes. Consider an emergency room on a day when 150 patients visit.
a.What is the probability that more than half will wait more than 30 minutes?
b.What is the probability that more than 80 will wait more than 30 minutes?
c.What is the probability that more than 60 but less than 90 will wait more than 30 minutes?
In: Statistics and Probability
Provide an appropriate response.
The distribution of incomes of employees at one company is strongly skewed to the right and the mean and standard deviation of the incomes are known. Is it possible to determine the probability that a randomly selected employee earns more than $80,000? Is it possible to determine the probability that the mean income for 10 randomly selected employees is more than $80,000? Is it possible to determine the probability that the mean income for 50 randomly selected employees is more than $80,000? Explain your responses.
In: Statistics and Probability
A new medical test has been designed to detect the presence of
the mysterious Brainlesserian disease. Among those who have the
disease, the probability that the disease will be detected by the
new test is 0.78. However, the probability that the test will
erroneously indicate the presence of the disease in those who do
not actually have it is 0.02. It is estimated that 19 % of the
population who take this test have the disease.
If the test administered to an individual is positive, what is the
probability that the person actually has the disease?
In: Statistics and Probability
The average loan amount issued by a small short-term lender is
$1080 with a standard deviation of $184. Determine the
probabilities, assuming that the population data is normally
distributed.
a) What is the probability that the lender issues more than $1150 to a random borrower?
b) What is the probability that the lender issues at most $1150, on average, to a random sample of 30 borrowers?
c) What is the probability that the lender issues between $1150 and $1175, on average, to a random sample of 30 borrowers?
In: Statistics and Probability
2. Suppose that a box is known to contain 50 red and 25 blue marbles. Two marbles are to be drawn in succession. The first marble is set aside and its color noted. It is not placed back into the box before the second marble is drawn.
a. Sketch a probability tree which represents this situation.
b. What is the probability that the second marble is red, if the first marble is red?
c. If the second marble is blue, what is the probability that the first marble is red?
In: Statistics and Probability
A survey of adults ages 18-29 found that 86% use the Internet. You randomly select 125 adults ages 18-29 and ask them if they use the Internet. (a) Find the probability that exactly 102people say they use the Internet. (b) Find the probability that at least 102people say they use the Internet. (c) Find the probability that fewer than 102people say they use the Internet. (d) Are any of the probabilities in parts (a)-(c) unusual? Explain.
In: Statistics and Probability
According to Consumer Response Annual Report, millennials spent an average of $103 on monthly dining in 2016. Let the amount spent on a monthly dining be normally distributed with unknown standard deviation. Assume that the probability of a randomly-selected millennial that spends more than $133 is 10%, and the probability that a randomly-selected millennial that spends less than $97 pounds is 40%. What is the probability that a randomly-selected millennial will spend between $73 and $109 on a monthly dining?
In: Statistics and Probability
According to a report by Scarborough Research, the average monthly household cellular phone bill is $73. Suppose local monthly household bills are normally distributed with a standard deviation of $11.35.
(a) What is the probability that a randomly selected monthly cellphone bill is between $60 and $74?
(b) What is the probability that a randomly selected monthly cellphone bill is between $79 and $88?
(c) What is the probability that a randomly selected monthly cellphone bill is no more than $39?
In: Statistics and Probability
Gears produced by a grinding process are categorized either as conforming (suitable for their intended purpose), degraded (unsuitable for the intended purpose but usable for another purpose), or scrap (not usable). Suppose that 75% of the gears produced are conforming, 11% are degraded, and 14% are scrap. Ten gears are selected at random.
What is the probability that eight or more are not scrap?
What is the probability that more than two are either degraded or scrap?
What is the probability that exactly nine are either conforming or degraded?
In: Statistics and Probability