Exam 6: The Normal Distribution and Other Continuous Distributions

If a data set is approximately normally distributed,its normal probability plot would be S-shaped.

TABLE 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 Table 6-3,what is the variance of the time interval?

The amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 15 minutes and a standard deviation of 2 minutes.The probability is ________ that a product is assembled in more than 19 minutes.

The value of the cumulative standardized normal distribution at Z is 0.6255.The value of Z is

The amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 15 minutes and a standard deviation of 2 minutes.So,90% of the products require more than ________ minutes for assembly.

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.The probability that Z is between -2.89 and -1.03 is ________.

A normal probability plot may be used to assess the assumption of normality for a particular set of data.

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?

TABLE 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 Table 6-5,what is the probability that a randomly selected orange will contain no more than 4.2 ounces of juices?

TABLE 6-6 According to Investment Digest,the arithmetic mean of the annual return for common stocks from 1926-2010 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 Table 6-6,find the probability that the annual return of a random year will be between 7.5% and 11%.

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?