Exam 6: The Normal Distribution and Other Continuous Distributions

If a particular set of data is approximately normally distributed,we would find that approximately

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.The probability that Z values are larger than ________ is 0.6985.

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 90?

Given that X is a normally distributed random variable with a mean of 50 and a standard deviation of 2,find the probability that X is between 47 and 54.

The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound.Assuming the weights of catfish are normally distributed,the probability that a randomly selected catfish will weigh less than 2.2 pounds is ________.

For some value of Z,the value of the cumulative standardized normal distribution is 0.2090.The value of Z is

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 less than 10 minutes?

Suppose the probability of finding a bark beetles-infested pine tree is the same anywhere over a piece of 100-acre national forest land.Which of the following distributions would you use to determine the probability of finding a bark beetles-infested pine tree in a piece of 10-acre national forest land?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.The probability that Z is less than -2.20 is ________.

The probability that a standard normal variable Z is positive is ________.

TABLE 6-4 The interval between consecutive hits at a website is assumed to follow an exponential distribution with an average of 40 hits per minute. -Referring to Table 6-4,what is the probability that the next hit at the website will occur between the next 1.2 and 1.5 seconds after just being hit by a visitor?

You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds.You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%.The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%.The probability is 20% that the time lapsed will be shorter how many seconds?

The probability that a particular brand of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8.A batch of 100,000 such alarms was produced by independent production lines.Which of the following distributions would you use to figure out the probability that at least 90,000 of them will function properly in case of a fire?

The true length of boards cut at a mill with a listed length of 10 feet is normally distributed with a mean of 123 inches and a standard deviation of 1 inch.What proportion of the boards will be between 121 and 124 inches?

TABLE 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 $2,000.At night he works 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 Table 6-2,for a given month,what is the probability that John's commission from the jewelry store is no more than $8,000?

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

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 between 16 and 21 minutes.

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?

The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound.A citation catfish should be one of the top 2% in weight.Assuming the weights of catfish are normally distributed,at what weight (in pounds)should the citation designation be established?

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 90 and 95?