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Statistics and Probability
Q.8 In a staff meeting called to address the problem of returned cheques at the supermarkets where you are interning as a financial analyst, the bank reports that 12 percent of all cheques are returned for insufficient funds, and of those, in those 50 percent of cases, there was cash given back to the customer. overall ,10 percent of customers ask for cash back at the end of their transaction with the store. For 1,000 customer visits, how many transactions will involve:
(f) insufficient funds? (g) Cash back to the customer? (h) Both insufficient funds and cashback? (i) Either insufficient funds or cash back?
(f) insufficient funds? (g) Cash back to the customer? (h) Both insufficient funds and cashback? (i) Either insufficient funds or cash back?
Statistics and Probability
HYPOTHESIS TESTING AND CONFIDENCE INTERVAL
3) Records on a fleet of trucks reveal that the average life of a set of spark plugs is normally distributed with a mean of 22,100 miles. The fleet owner purchased 18 sets and found that the sample average life was 23,400 miles; the sample standard deviation was 1,412 miles. To decide if the sample data support the company records that the spark plugs average 22,100 miles, state your decision in terms of the null hypothesis. Use a 0.05 level of significance.
4)A local grocery store wants to estimate the mean daily number of gallons of milk sold to customers. Assume the number of gallons sold follows the normal distribution, with a population standard deviation of 5.10 gallons. A random sample of 60 days shows that the mean daily number of gallons sold is 10.00. What is the point estimate of the population mean?
Statistics and Probability
We have a bag that contains 2red balls,3 blue balls and 4 green balls.For our first experiment,we take a random ball from the bag, observing its color, return the ball. To the bag and then take a second ball at random, observing its color
Describe the sample space and event space
Describe the sample space and event space
Statistics and Probability
A process was designed to cut metal rods for use in an assembly of mechanical devices. The lengths of the metal rods cut are approximately normally distributed with a mean of 2.20 cm and a standard deviation of 0.04 cm. If a particular type of mechanical device requires metal rods with lengths between 2.22 and 2.25 cm, what percentage of the metal rods would be expected to be rejected?
Statistics and Probability
a. The probability of success on any trial of a binomial
experiment is 25%. Find the probability
that the proportion of successes in a sample of
500 is less than 22%.
b. Repeat part (a) with n = 800.
c. Repeat part (a) with n = 1,000.
experiment is 25%. Find the probability
that the proportion of successes in a sample of
500 is less than 22%.
b. Repeat part (a) with n = 800.
c. Repeat part (a) with n = 1,000.
Statistics and Probability
The amount of time spent by North American
adults watching television per day is normally distributed
with a mean of 6 hours and a standard
deviation of 1.5 hours.
a. What is the probability that a randomly selected
North American adult watches television for
more than 7 hours per day?
b. What is the probability that the average time
watching television by a random sample of five
North American adults is more than 7 hours?
c. What is the probability that in a random sample
of five North American adults, all watch television
for more than 7 hours per day?
adults watching television per day is normally distributed
with a mean of 6 hours and a standard
deviation of 1.5 hours.
a. What is the probability that a randomly selected
North American adult watches television for
more than 7 hours per day?
b. What is the probability that the average time
watching television by a random sample of five
North American adults is more than 7 hours?
c. What is the probability that in a random sample
of five North American adults, all watch television
for more than 7 hours per day?
Statistics and Probability
A factory’s worker productivity is normally distributed.
One worker produces an average of 75 units
per day with a standard deviation of 20. Another
worker produces at an average rate of 65 per day
with a standard deviation of 21. What is the probability
that in 1 week (5 working days), worker 1
will outproduce worker 2?
One worker produces an average of 75 units
per day with a standard deviation of 20. Another
worker produces at an average rate of 65 per day
with a standard deviation of 21. What is the probability
that in 1 week (5 working days), worker 1
will outproduce worker 2?
Statistics and Probability
a. The manufacturer of aspirin claims that the proportion
of headache sufferers who get relief with
just two aspirins is 53%. What is the probability
that in a random sample of 400 headache sufferers,
less than 50% obtain relief? If 50% of the
sample actually obtained relief, what does this
suggest about the manufacturer’s claim?
b. Repeat part (a) using a sample of 1,000
of headache sufferers who get relief with
just two aspirins is 53%. What is the probability
that in a random sample of 400 headache sufferers,
less than 50% obtain relief? If 50% of the
sample actually obtained relief, what does this
suggest about the manufacturer’s claim?
b. Repeat part (a) using a sample of 1,000
Statistics and Probability
9.18 Given a normal population whose mean is 50 and
whose standard deviation is 5, find the probability
that a random sample of
a. 4 has a mean between 49 and 52.
b. 16 has a mean between 49 and 52.
c. 25 has a mean between 49 and 52.
whose standard deviation is 5, find the probability
that a random sample of
a. 4 has a mean between 49 and 52.
b. 16 has a mean between 49 and 52.
c. 25 has a mean between 49 and 52.
Statistics and Probability
A sample of n = 16 observations is drawn from a
normal population with μ = 1,000 and σ = 200.
Find the following.
a. P(X > 1,050)
b. P(X < 960)
c. P(X > 1,100)
normal population with μ = 1,000 and σ = 200.
Find the following.
a. P(X > 1,050)
b. P(X < 960)
c. P(X > 1,100)
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#340153 on Dec 2023
#340153 on Dec 2023