Exam 6: The Normal Probability Distribution

The mean of any normal distribution is always zero.

Using the standard normal curve, the z-score representing the 10th percentile is 1.28.

The lifespan of salmon flies is normally distributed with a mean of 60 days and a standard deviation of 20 days. What percentage of a salmon fly population lives less than 12 days? ______________ What percentage of a salmon fly population lives between 80 and 101 days? ______________ Find the value x₀ such that 6.3% of a salmon fly population live less than x₀ days. ______________

In a certain population, 18% of the people have Rh-negative blood. A blood bank serving this population receives 95 blood donors on a particular day. What is the probability that 10 or fewer are Rh-negative? ______________ What is the probability that 15 to 20 (inclusive) of the donors are Rh-negative? ______________ What is the probability that more than 80 of the donors are Rh-positive? ______________

If z is a standard normal random variable, the area between z = 0.0 and z = 1.25 compared to the area between z = 1.25 and z = 2.5 will be:

Let be a z-score that is unknown but identifiable by position and area. If the area to the right of is 0.8849, the value of is 1.2.

Mean, median, and mode are:

Even though the normal probability distribution deals with continuous variables, we can use it to approximate the binomial whenever np > 5 and also nq > 5.

For a continuous random variable x, P(6 < x < 8) is represented by the area under the probability function over the interval from 6 to 8.

For a continuous random variable x, P(x a) = P(x > a) and P(x a) = P(x < a).

Given that X is a binomial random variable, the binomial probability P(X = x) is approximated by the area under a normal curve between:

Consider a binomial random variable x with n = 25 and p = 0.01. Would the normal approximation be appropriate here? ______________ Why or why not? ________________________________________________________

The time it takes Jessica to bicycle to school is normally distributed with mean 15 minutes and variance 4. Jessica has to be at school at 8:00 am. What time should she leave her house so she will be late only 4% of the time?

For any continuous random variable x, P(x = 5) = 1 is always true.

Suppose z has a standard normal distribution. Then 85.08% of the possible z values are smaller than: ______________

Suppose the amount of heating oil used annually by households in Iowa is normally distributed with mean 200 gallons per household per year and standard deviation 40 gallons of heating oil per household per year. What is the probability a randomly selected Iowa household uses more than 150 gallons of heating oil per year? ______________ What is the probability a randomly selected Iowa household uses between 180 and 300 gallons per year? ______________ If the members of a particular household were scared into using fuel conservation measures by newspaper accounts of the probable price of heating oil next year, and they decided they wanted to use less oil than 97.5% of all other Iowa households currently using heating oil, what is the maximum amount of oil they can use and still accomplish their conservation objective? ______________

Which of the following distributions is considered the cornerstone distribution of statistical inference?

Given that z is a standard normal random variable, a value of z that is equal to zero indicates that the standard deviation of z is zero also.

Given that Z is a standard normal random variable, a negative value of Z indicates that the standard deviation of Z is negative.

Which of the following statements about continuous random variables is correct?