Exam 7: Continuous Probability Distributions

In a paper mill,which produces newsprint from Southern Pine,the production manager finds a flaw for each 1000 feet of newsprint.He knows that the outcome is a Poisson process with a continuous distribution.A group of visitors is touring the plant.After arriving at the final stage of production,if they remain long enough to observe 330 feet of newsprint produced,what is the probability that they will miss seeing the next defect?

Which of the following statements are true regarding the areas beneath any normal curve?

What does it mean when we say a random variable is standardized?

Suppose the monthly demand for automobile tires at a tire dealer is normally distributed with a mean of 250 tires and a standard deviation of 50 tires.How many tires must the store have in inventory at the beginning of each month in order to meet demand 95 percent of the time?

Determine P(z ≥ 1.58)for the standard normal curve.

The z-score representing the 10th percentile of the standard normal distribution is:

Assume x is normally distributed with mean $\mu$ = 15 and standard deviation $\text { σ }$ = 3.Use the approximate areas beneath the normal curve,as discussed in this section,to find P(12 ≤ x ≤ 18).

Continuous probability distributions describe probabilities associated with random variables that can take on any value along a given range or continuum and for which there are no gaps between these possible values.

Express in your own words the procedure for finding the area under the standard normal curve between z = 0 and z = 1.53.

If the random variable x is exponentially distributed with parameter $\lambda$ = 4,then P(x ? 0.25),up to 4 decimal places,is:

In the normal distribution,the curve is asymptotic but never intercepts the horizontal axis either to the left or right.

Why is it important to use the correction for continuity when approximating binomial probabilities with the normal distribution?

A manufacturer of nails packages 16-penny nails in 25-pound boxes.Filling of the boxes is automated with the dispenser set to an average of 25.1 pounds with a standard deviation of 0.25 pounds.One 25-pound box of 16-penny nails is included in the estimate for a remodeling contract by a local builder.What is the probability that the box purchased will have less than the required 25 pounds?

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 = 6).

If the random variable x is exponentially distributed with parameter $\lambda$ = 1.5,then P(2 ? x ? 4),up to 4 decimal places,is:

Given that z is a standard normal random variable,and that the area to the right of z is 0.9066,then the value of z must be:

A zipper manufacturer has found that 1.5% of its zippers are defective.The company averages 4982 zippers per day.The probability of finding between 90 and 100 defects in a given day is:

In 2000,the average charge of tax preparation was $95.Assuming a normal distribution and a standard deviation of $10,use the approximate areas beneath the normal curve,as discussed in this section,to answer: What proportion of tax preparation fees were between $85 and $105?

A retailer finds that the demand for a very popular board game averages 100 per week with a standard deviation of 20.If the seller wishes to have adequate stock 95% of the time,how many of the games must she keep on hand?

The total area beneath the curve of any continuous distribution is ____________________.