Exam 6: The Normal Distribution and Other Continuous Distributions

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.

As a general rule,one can use the normal distribution to approximate a binomial distribution whenever the sample size is at least 30.

As a general rule,one can use the normal distribution to approximate a binomial distribution whenever the sample size is at least 15.

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 between 10 and 15 minutes?

Instruction 6-7 A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.15. -Referring to Instruction 6-7 and assuming that the number of computers that requires repair on a given day follows a binomial distribution,compute the probability that there will be no more than 8 computers that require repair on a given day using a normal approximation.

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.So 27% of the possible Z values are smaller than ________.

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).

The exponential and Poisson distributions are closely related.

Instruction 6-4 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 Instruction 6-4,the probability is 0.95 that John's commission from the jewelry store is at least how much in a given month?

The amount of pyridoxine (in grams)in a multiple vitamin is normally distributed with μ = 110 grams and σ = 25 grams.What is the probability that a randomly selected vitamin will contain less than 100 grams or more than 120 grams of pyridoxine?

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

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 ________.

Instruction 6-4 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 Instruction 6-4,the probability is 0.25 that John's income as a waiter is no more than how much in a given month?

Instruction 6-2 The city manager of a large city believes that the number of reported accidents on any weekend has a normal distribution.She takes a sample of nine weekends and determines the number of reported accidents during each.The ordered array for this data is: 15,46,53,54,55,76,82,256,407. -Referring to Instruction 6-2,the seventh standard normal quantile is ________.

The owner of a fish market determined that the average weight for a rainbow trout is 3.2 kilograms with a standard deviation of 0.8 kilogram.Assuming the weights of rainbow trout are normally distributed,the probability that a randomly selected rainbow trout will weigh more than 4.4 kilograms is ________.

Instruction 6-4 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 Instruction 6-4,John's commission from the jewelry store will be between what two values symmetrically distributed around the population mean 90% of the time?

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 0.3483.

The amount of pyridoxine (in grams)in a multiple vitamin is normally distributed with μ = 110 grams and σ = 25 grams.Approximately 83% of the vitamins will have at least how many grams of pyridoxine?

Times spent watching TV every week by primary school students follow an exponential distribution with mean 10 hours.The probability that a given primary school student spends between 10 and 15 hours watching TV is ________.

A food processor packages orange juice in small jars.The weights of the filled jars are approximately normally distributed with a mean of 336 grams and a standard deviation of 9.6 grams.Find the proportion of all jars packaged by this process that have weights that fall below 348 grams.