Exam 7: Continuous Probability Distributions

Assume the standard normal curve and determine the probability or area between z = -1.28 and z = 1.28.

Using the standard normal curve,find the area between z = 0 and z = 3.3. $\approx$ ____________________.

The selling price of various homes in a community follows the normal distribution with a mean of $176,000 and a standard deviation of $22,300.What is the probability that the next house will sell for less than $190,000?

A manufacturer produces Walkman tap players/radios.The electronic components are positioned in the outer case after the case has been given an epoxy finish.The production manager must time the drying process with the total assembly line and therefore must determine the appropriate drying time.An intensive cost analysis indicated that a risk of just 0.3% of the cases being wet and therefore smudged was acceptable.If drying times are normally distributed with a mean of 3.6 minutes and a standard deviation of 0.6 minutes,what time setting should the production manager set for the automatic timer which controls the production line? ____________________ minutes

Suppose that x is a binomial random variable with n = 100 and $\pi$ = 0.18.Employ the normal approximation to find P(15 ≤ x ≤ 21).

A circus performer who gets shot from a cannon is supposed to land in a safety net positioned at the other end of the arena.The distance he travels is normally distributed with a mean of 175 feet and a standard deviation of 15 feet.His landing net is 50 feet long and the mid-point of the net is positioned 175 feet from the cannon.What is the probability that the performer will hit the net on a given night?

If a computer statistical package were to simulate 500 random observations from a normal distribution with mean $\mu$ = 100 and standard deviation $\text { σ}$ = 50,what percentage of these observations would you expect to have a value of 200 or more? Do you think the actual number in the " ≥ 200" range would equal the expected number in this range? If so,why? If not,why not?

Assuming a standard normal distribution,determine P(z ≤ -0.75).

A large mail house which mails such items as catalogues,magazines,and other bulk mailings guarantees that there will be no more than a 3% error rate on its mailing labels.A customer who contracted a mailing to 190,000 individuals experienced a return of 5,900 items,which had incorrect addresses.Which of the following statements is true?

What are the mean and standard deviation of a normally distributed random variable,which has been "standardized"? Mean = ____________________ SD = ____________________

Using the standard normal table,the total area between z = -1.82 and z = -1.38 is:

The time it takes a technician to fix a computer problem is exponentially distributed with a mean of 15 minutes.What is the probability that it will take a technician between 10 to 15 minutes to fix a computer problem?

The speed of cars passing through a checkpoint follows a normal distribution with a mean of 62.6 miles per hour and a standard deviation of 3.7 miles per hour.What is the probability that the next car passing by will be traveling between 61 and 70 miles per hour?

For any specified interval of values,the probability that a continuous random variable x will assume a value within the interval is the area beneath the curve between the two points describing the interval.

An efficiency expert makes periodic checks for weighting errors for a long distance shipping firm.The expert inspects for errors in weighing,in recording weights,and errors in processing the bills of lading.Based on past records,the number of weekly errors for all shipments averages 5.30 with a standard deviation of 1.23,and the frequency histogram approximates a normal distribution.Suppose x is the number of weighing errors that will occur next week. Compute the approximate probability for (x ≤ 2).

Determine P(-2.45 ≤ z ≤ 1.69),assuming a standard normal distribution.

The time it takes a technician to fix a computer problem is exponentially distributed with a mean of 15 minutes.What is the variance of the time it takes a technician to fix a computer problem? ____________________ minutes

The binomial distribution is symmetrical whenever the population proportion $\pi$ is ____________________,and approaches symmetry for values that are close to ____________________.

A coin is flipped 14 times.Using the normal distribution,calculate the probability of observing either 4,5,or 6 heads.

If z is a standard normal random variable,find the value z₁ for which: A)P(0 ≤ z ≤ z₁)= 0 .276 B)P(z ≥ z₁)= 0.341 C)P(z ≥ z₁)= 0.819 D)P(-z₁ ≤ Z ≤ z₁)= 0.785