Exam 6: The Normal Distribution and Other Continuous Distributions

Suppose that past history shows that 60% of university students prefer Pepsi .A sample of 10,000 students is to be selected.Which of the following distributions would you use to figure out the probability that at least half of them will prefer Pepsi ?

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 _________.

In the game Wheel of Fortune,which of the following distributions can best be used to compute the probability of winning the special vacation package in a single spin?

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,90% of the products require more than _________minutes for assembly.

For some value of Z,the probability that a standard normal variable is below Z is 0.2090.The value of Z is

Instruction 6.7 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 Instruction 6.7,what is the probability that the next hit at the website will occur within 10 seconds after just being hit by a visitor?

Define uniform (or rectangular)distribution.

The true length of boards cut at a mill with a listed length of 3 metres is normally distributed with a mean of 303 cm and a standard deviation of 1 cm -What proportion of the boards will be over 305 cm in length?

The probability that a standard normal random variable,Z,is between 1.50 and 2.10 is the same as the probability Z is between −2.10 and −1.50.

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 $9,000 and $11,000?

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 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?

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 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.

Times spent using a tablet or smartphone 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 using a tablet or smartphone is _______

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 at least 25 computers that require repair on a given day using a normal approximation.

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 less than 100 grams or more than 120 grams of pyridoxine?

If we know that the length of time it takes a university student to find a parking space in the university car park 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 university student will take between 2 and 4.5 minutes to find a parking space in the car park.

If a data batch is approximately normally distributed,its normal probability plot would be S-shaped.

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 $5,000 and $7,000?