Exam 6: The Normal Distribution and Other Continuous Distributions

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?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of The probability that Z is less than 1.15 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, 70% of the products would be assembled within ______ minutes.

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 middle 86% of the time lapsed will fall between which two numbers?

As a general rule, one can use the normal distribution to approximate a binomial distribution whenever np is at least 5.

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, 15% of the products require more than __________minutes for assembly.

TABLE 6-4 John has two jobs. For daytime work at a jewelry store he is paid $200 per month, plus a commission. His monthly commission is normally distributed with mean $600 and standard deviation $40. At night he works as a waiter, for which his monthly income is normally distributed with mean $100 and standard deviation $30. John's income levels from these two sources are independent of each other. -Referring to Table 6-4, for a given month, what is the probability that John's total income from these two jobs is less than $825?

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, find the probability that a randomly selected college student will take between 2 and 4.5 minutes to find a parking spot in the library parking lot.

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 75 and 90?

Patients arriving at an outpatient clinic follow 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?

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 greater than 95?

TABLE 6-5 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 6-5, what is the probability that the time interval between two consecutive defective light bulbs will be between 10 and 35 minutes?

To determine the probability of getting more than 3 events of interest in a binomial distribution, you will find the area under the normal curve for X = 3.5 and above.

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?

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 less than 12 minutes.

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 amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with µ = 110 grams and a = 25 grams. What is the probability that a randomly selected vitamin will contain less than 100 grams of pyridoxine?

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 86.64% of the students will score between which two scores?

Times spent watching TV every week by first graders follow an exponential distribution with mean 10 hours. The probability that a given first grader spends less than 20 hours watching TV is______ .

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of The probability that Z values are larger than is ______0.6985.