Find the area under the standard normal curve

Assignment Help Basic Statistics

Reference no: EM132597698

Question 1:
Tommy Wait, a minor league baseball pitcher, is notorious for taking an excessive amount of time between pitches. In fact, his times between pitches are normally distributed with a mean of 34 seconds and a standard deviation of 2.7 seconds. What percentage of his times between pitches are longer than 39 seconds?

Round your answer to two decimal places.

The time between pitches is longer than 39 seconds _____% of the time.

Question 2:
Obtain the following probability for the standard normal distribution. Round your answer to four decimal places.
P(-2A6 ≤ z ≤ 1.27) =

Question 3:
Find the area under the standard normal curve to the left of z = 0.88. Round your answer to four decimal places.

Question 4:
Find the area under the standard normal curve to the right of = -0.68.
Round your answer to four decimal places.
A=

Question 5:
Compute the area under the standard normal curve. Round your answers to four decimal places.
(a) The area to the right of r = 1.73 equals
(b) The area to the left of z = - 1.3 equals
(c) The area between z = 0 and z = 3.15 equals

Question 6:
Let.t be a continuous random variable that is normally distributed with a mean of 42 and a standard deviation of l7. Find the probability that.t assumes a value less than 47. Round your answer to four decimal places.

P =

Question 7:
The Bank of Connecticut issues Visa and MasterCard credit cards. It is estimated that the balances on all Visa credit cards issued by the Bank of Connecticut have a mean of $845 and a standard deviation of $275. Assume that the balances on all these Visa cards follow a normal distribution.

a. What is the probability that a randomly selected Visa card issued by this bank has a balance between $950 and $1470?
Round your answer to three decimal places.

b. What percentage of the Visa cards issued by this bank have a balance of $730 or more?
Round your answer to two decimal places.

P =

Question 8:
According to the records of an electric company serving the Boston area, the mean electric consumption for all households during winter is 1650 kilowatt-hours per month. Assume that the monthly electric consumptions during winter by all households in this area have a normal distribution with a mean of 1650 kilowatt-hours and a standard deviation of 320 kilowatt-hours. What percentage of the households in this area have a monthly electric consumption of 1824 to 1991 kilowatt-hours?

Round your answer to two decimal places.

Question 9:
Find the value of z so that the area under the standard normal curve from 0 to z is 0.4641 and z is negative. Round your answer to two decimal places.
Z=

Question 10:
Determine the value of z so that the area under the standard normal curve
(a) in the right tail is 0.0305. Round the answer to two decimal places.
z=
(b) in the left tail is 0.0457. Round the answer to two decimal places.
z=

Question 11:
Fast Auto Service provides oil and lube service for cars. It is known that the mean time taken for oil and lube service at this garage is 15 minutes per car and the standard deviation is 2.4 minutes. The management wants to promote the business by guaranteeing a maximum waiting time for its customers. If a customers car is not serviced within that period, the customer will receive a 50% discount on the charges. The company wants to limit this discount to at most 2% of the customers. What should the maximum guaranteed waiting time be? Assume that the times taken for oil and lube service for all cars have a normal distribution.

Round your answer to the nearest minute.
The maximum guaranteed waiting time should be approximately _____ minutes.

Question 12:
The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $115 and a standard deviation of $17. If the management wants to give free gifts to at most 14.46% of the customers, what should the amount be above which a customer would receive a free gift?
Round your answer to two decimal places.

A customer should spend at least $ ______ to receive a free gift.

Question 13:
A machine at Keats Corporation fills 64-ounce detergent jugs. The machine can be adjusted to pour, on average, any amount of detergent into these jugs. However, the machine does not pour exactly the same amount of detergent into each jug; it varies from jug to jug. It is known that the net amount of detergent poured into each jug has a normal distribution with a standard deviation of 0.35 ounce. The quality control inspector wants to adjust the machine such that at least 95% of the jugs have more than 64 ounces of detergent. What should the mean amount of detergent poured by this machine into these jugs be?
Round your answer to 2 decimal places.
ounces

Question 14:
According to a U.S. Census American Community Survey, 5.59% of workers in Portland, Oregon, commute to work on their bicycles. Find to 4 decimal places the probability that in a sample of 400 workers from Portland, Oregon, the number who commute to work on their bicycles is 24 to 29.
Probability =
the absolute tolerance is +1-0.003

Question 15:
According to a survey, 15% of U.S. adults with online services currently read e-books. Assume that this percentage is true for the current population of U.S. adults with online services. Find to 4 decimal places the probability that in a random sample of 600 U.S. adults with online services, the number who read e-books is
a. exactly 96. Probability =
b. at most 112. Probability
c. 62 to 107. Probability

Reference no: EM132597698

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