Exam 6: The Normal Distribution and Other Continuous Distributions

The amount of pyridoxine (in grams)in a multiple vitamin is normally distributed with $\mu$ = 110 grams and $\sigma$ 25 grams. -What is the probability that a randomly selected vitamin will contain at least 100 grams of pyridoxine?

Instruction 6.2 John has two jobs. For daytime work at a jewellery 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 6.2,for a given month,what is the probability that John's commission from the jewellery store is between $11,000 and $12,000?

As a general rule,one can use the normal distribution to approximate a binomial distribution whenever n(1−p)is at least 5.

Instruction 6.6 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 Instruction 6.6,the probability is 90% that the time interval between two consecutive defective light bulbs will fall between which two values that are the same distance from the mean?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. -So 85% of the possible Z values are smaller than _________.

Which of the following about the normal distribution is NOT true?

Which distribution is also known as the rectangular distribution?

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1 patient per hour.What is the probability that a randomly chosen arrival to be more than 2.5 hours?

Instruction 6.8 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 6.8 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.

Instruction 6.5 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 6.5,construct a normal probability plot.

A food processor packages green olives 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 above 350.4 grams.

In its standardised form,the normal distribution

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,above what weight (in kilograms)do 89.80% of the weights occur?

Instruction 6.6 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 Instruction 6.6,what is the probability that the time interval between two consecutive defective light bulbs will be between 10 and 20 minutes?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. -The probability that Z is between -0.88 and 2.29 is _________.

Instruction 6.2 John has two jobs. For daytime work at a jewellery 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 6.2,the probability is 0.35 that John's income as a waiter is no less than how much in a given month?

A catalogue company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product.The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3 minutes. -What proportion of customers having to hold more than 1.5 minutes will hang up before placing an order?

One of the reasons that a correction for continuity adjustment is needed when approximating the binomial distribution with a normal distribution is because the probability of getting a specific value of a random variable is zero with the normal distribution.

Instruction 6.6 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 Instruction 6.6,what is the standard deviation of the time interval?

A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan.Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years.What proportion of the plan recipients die before they reach the standard retirement age of 65?