Exam 6: The Normal Distribution and Other Continuous Distributions

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. -The owner of a fish market determined that the average weight for a catfish is 3.2 pounds.He also knew that the probability of a randomly selected catfish that would weigh more than 3.8 pounds is 20% and the probability that a randomly selected catfish that would weigh less than 2.8 pounds is 30%.The middle 40% of the catfish will weigh between ________ pounds and ________ pounds.

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?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.So,50% of the possible Z values are between ________ and ________ (symmetrically distributed about the mean).

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 60% of the time lapsed will fall between which two numbers?

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 within 10 seconds after just being hit by a visitor?

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 probability that the time interval between two consecutive defective light bulbs will be at least 90 minutes?

Let X represent the amount of time till 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 per minute),find the probability that it will take between 2 and 12 minutes for the next student to arrive at the library parking lot.

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 more than 11 minutes.

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.The probability that Z is between -2.33 and 2.33 is ________.

TABLE 6-1 The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with a population mean of 320 and a population standard deviation of 20 inches. -Referring to Table 6-1,for a randomly chosen Monday the probability is 0.1 that there will be less than how many column inches of classified advertisements?

A wheel spinning game is played with a special wheel with 24 equal segments that determine the dollar values of a single spin.Which of the following distributions can best be used to compute the probability of winning a specific dollar value in a single spin?

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 a mean of $10,000 and a standard deviation of $2,000.At night he works occasionally as a waiter,for which his monthly income is normally distributed with a mean of $1,000 and a standard deviation of $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 income as a waiter is between $800 and $900?

TABLE 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 Table 6-6,find the probability that the annual return of a random year will be more than 11.5%.

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.The probability that Z is less than 1.15 is ________.

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 a mean of $10,000 and a standard deviation of $2,000.At night he works occasionally as a waiter,for which his monthly income is normally distributed with a mean of $1,000 and a standard deviation of $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 at least $12,000?

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 13 and 16 seconds?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.The probability that Z is more than -0.98 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 14 and 16 minutes.

The value of the cumulative standardized normal distribution at Z is 0.8770.The value of Z is

TABLE 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 Table 6-6,10% of the annual returns will be less than what amount?