Exam 6: The Normal Distributions and Other Continuous Distributions

You were told that the mean score on a statistics exam is 75 with the scores normally distributed.In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%.What is the probability of a score between 60 and 95?

If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, 75.8% of the college students will take more than how many minutes when trying to find a parking spot in the library parking lot?

SCENARIO 6-2 John has two jobs.For daytime work at a jewelry store he is paid $15,000 per month, plus a commission.His monthly commission is normally distributed with mean $10,000 and standard deviation $2000.At night he works occasionally as a waiter, for which his monthly income is normally distributed with mean $1,000 and standard deviation $300.John's income levels from these two sources are independent of each other. -Referring to Scenario 6-2, for a given month, what is the probability that John's income as a waiter is at least $1400?

The value of the cumulative standardized normal distribution at 1.5X is 0.9332.The value of X is

The amount of time necessary for assembly line workers to complete a product is a normal variable with a mean of 15 minutes and a standard deviation of 2 minutes.The probability is __________ that a product is assembled in between 16 and 21 minutes.

You were told that the mean score on a statistics exam is 75 with the scores normally distributed.In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%.The middle 95.46% of the students will score between which two scores?

SCENARIO 6-6 According to Investment Digest, the arithmetic mean of the annual return for common stocks over an 85-year period was 9.5% but the value of the variance was not mentioned.Also 25% of the annual returns were below 8% while 65% of the annual returns were between 8% and 11.5%. The article claimed that the distribution of annual return for common stocks was bell-shaped and approximately symmetric.Assume that this distribution is normal with the mean given above. Answer the following questions without the help of a calculator, statistical software or statistical table. -Referring to Scenario 6-6, 10% of the annual returns will be at least what amount?

The interval between patients arriving at an outpatient clinic follows an exponential distribution at a rate of 1 patient per hour.What is the probability that a randomly chosen arrival to be less than 20 minutes?

You were told that the amount of time elapsed between consecutive trades on a foreign stock exchange market followed a normal distribution with a mean of 15 seconds.You were also told that the probability that the time elapsed between two consecutive trades to fall between 16 to 17 seconds was 13%.The probability that the time elapsed between two consecutive trades would fall below 13 seconds was 7%.What is the probability that the time elapsed between two consecutive trades will be between 14 and 17 seconds?

Any set of normally distributed data can be transformed to its standardized form.

The interval between patients arriving at an outpatient clinic follows an exponential distribution at a rate of 1.5 patients per hour.What is the probability that a randomly chosen arrival to be between 10 and 15 minutes?

SCENARIO 6-5 A company producing orange juice buys all its oranges from a large orange orchard.The amount of juice that can be squeezed from each of these oranges is approximately normally distributed with a mean of 4.7 ounces and some unknown standard deviation.The company's production manager knows that the probability is 30.85% that a randomly selected orange will contain less than 4.5 ounces of juice.Also, the probability is 10.56% that a randomly selected orange will contain more than 5.2 ounces of juice.Answer the following questions without the help of a calculator, statistical software or statistical table. -Referring to Scenario 6-5, what is the probability that a randomly selected orange will contain more than 4.2 ounces of juices?

The amount of time necessary for assembly line workers to complete a product is a normal variable with a mean of 15 minutes and a standard deviation of 2 minutes.The probability is __________ that a product is assembled in between 14 and 16 minutes.

The interval between patients arriving at an outpatient clinic follows an exponential distribution at a rate of 1 patient per hour.What is the probability that a randomly chosen arrival to be more than 1 hour?

SCENARIO 6-2 John has two jobs.For daytime work at a jewelry store he is paid $15,000 per month, plus a commission.His monthly commission is normally distributed with mean $10,000 and standard deviation $2000.At night he works occasionally as a waiter, for which his monthly income is normally distributed with mean $1,000 and standard deviation $300.John's income levels from these two sources are independent of each other. -Referring to Scenario 6-2, John's income as a waiter will be between what two values symmetrically distributed around the population mean 80% of the time?

Let X represent the amount of time until the next student will arrive in the library parking lot at the university.If we know that the distribution of arrival time can be modeled using an exponential distribution with a mean of 4 minutes (i.e.the mean number of arrivals is 1/4 per minute), find the probability that it will take more than 10 minutes for the next student to arrive at the library parking lot.

SCENARIO 6-3 Suppose the time interval between two consecutive defective light bulbs from a production line has a uniform distribution over an interval from 0 to 90 minutes. -Referring to Scenario 6-3, what is the probability that the time interval between two consecutive defective light bulbs will be exactly 10 minutes?

SCENARIO 6-3 Suppose the time interval between two consecutive defective light bulbs from a production line has a uniform distribution over an interval from 0 to 90 minutes. -Referring to Scenario 6-3, what is the probability that the time interval between two consecutive defective light bulbs will be at least 80 minutes?

SCENARIO 6-6 According to Investment Digest, the arithmetic mean of the annual return for common stocks over an 85-year period was 9.5% but the value of the variance was not mentioned.Also 25% of the annual returns were below 8% while 65% of the annual returns were between 8% and 11.5%. The article claimed that the distribution of annual return for common stocks was bell-shaped and approximately symmetric.Assume that this distribution is normal with the mean given above. Answer the following questions without the help of a calculator, statistical software or statistical table. -Referring to Scenario 6-6, find the probability that the annual return of a random year will be between 7.5% and 11%.

You were told that the mean score on a statistics exam is 75 with the scores normally distributed.In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%.What is the probability of a score between 55 and 95?