Exam 6: The Normal Probability Distribution

The mayor of the city of Detroit was informed that household water usage was a normally distributed random variable with a mean of 25 gallons and a standard deviation of 4 gallons per day. Find the probability that a random chosen household uses more than 23 gallons per day. ______________ Find the probability that a randomly chosen household uses between 20 and 25 gallons per day. ______________ Find the probability that a randomly chosen household uses fewer than 21 gallons per day. ______________ If the mayor wants to give a tax rebate to the 20% lowest water users, what should the gallons per day cutoff be? ______________ The mayor advertised on a local TV channel for about three weeks his intention to give a tax rebate to the 20% lowest water users. If the advertisement lowered the mean usage of 25 gallons to 21 gallons, what should the gallons per day cutoff be? ______________

If the random variable x is normally distributed with a mean equal to .45 and a standard deviation equal to .40, then P(x .75) is:

A smooth frequency curve that describes the probability distribution of a continuous random variable is called a standard normal curve.

For the standard normal distribution, find the value z₁ such that: P(-z₀ > z > z₀) = 0.966 ______________ P(z > z₀) = 0.0174 ______________ P(z > z₀) = 0.5398 ______________

The possible observations about continuous random variables are infinite in number; characteristics measured in units of money, time, distance, height, volume, length, or weight exemplify the matter.

Let x be a continuous random variable and let c be a constant. Which of the following statements is false?

Adding or subtracting 0.5 from the binomial random variable x's interval endpoints (i.e., the so-called continuity correction) improves the normal approximation to the binomial by correcting for or accounting for the "missing" corners of the probability rectangles corresponding to values of x.

Any continuous random variable cannot take on negative values.

The normal approximation to the binomial is appropriate when the number of trials n is large and the probability of success p is near 0.05.

The shape of the normal probability distribution is determined by the population standard deviation . Small values of reduce the height of the curve and increase the spread; large values of increase the height of the curve and reduce the spread.

The total area under any continuous probability curve is equal to one.

A continuous random variable x is normally distributed with a mean of 1200 and a standard deviation of 150. Given that x = 1410, its corresponding z-score is 1.40.

Twenty percent of American men over 30 have high blood pressure. To run an experiment, a researcher needs to identify at least 15 men with high blood pressure. If the researcher examines 100 men over 30, what is the approximate probability he or she finds enough men with high blood pressure to run the experiment? ______________

Past records indicate 60% of the eligible voters in Michigan vote in the primary election. What is the expected number in a random sample of 200 eligible voters who will vote in the next primary? ______________ What is the approximate probability more than 150 from a sample of 200 will vote in the next primary? ______________

Using the standard normal curve, the probability or area between z = -1.28 and z = 1.28 is 0.3997.

A standard normal distribution is a normal distribution with:

The relative frequency associated with a particular class in the population is the probability of drawing a measurement from that class.

Continuous random variables that can assume values at all points on an interval of values, with no breaks between possible values, are quite common. Examples include:

Suppose x is normally distributed with a mean of 75 and a standard deviation of 4. Would it be unusual to observe a value x = 59? ______________ Explain. ________________________________________________________

If the random variable X is normally distributed with a mean of 75 and a standard deviation of 8, then P(X 75) is: