Exam 8: Continuous Probability Distributions

Suppose it is known that 60% of students at a particular university are smokers. A sample of 500 students from the university is selected at random. Approximate the probability that less than 280 of these students are smokers.

Given that Z is a standard normal random variable, P(-1.23 $\le$ Z $\le$ 1.89) is:

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

The length of time patients must wait to see a doctor at an emergency room in a large hospital is uniformly distributed between 40 minutes and 3 hours. a. What is the probability that a patient would have to wait between 50 minutes and 2 hours? b. What is the probability that a patient would have to wait exactly 1 hour? c. Find the expected waiting time. d. Find the standard deviation of the waiting time.

The probability density function f(x) of a random variable X that is normally distributed is completely determined once the:

Given that Z is a standard normal variable, the value z for which P(Z $\le$ z) = 0.2580 is:

Let X be an exponential random variable with $\lambda$ = 2.50. Find the following probabilities. a. P(X $\geq$ 1.5). b. P(X $\leq$ 1). c. P(0.25 $\leq$ X $\leq$ 0.78). d. P(X = 0.41).

Researchers studying the effects of a new diet found that the weight loss over a one-month period by those on the diet was normally distributed with a mean of 7 kg and a standard deviation of 2.5 kg. a. What proportion of the dieters lost more than 10 kg? b. What proportion of the dieters gained weight? c. If a dieter is selected at random, what is the probability that the dieter lost at most 5 kg?

The normal approximation to the binomial distribution works best when the number of trials is large, and when the binomial distribution is symmetrical (like the normal).

Given that X is a normal variable, which of the following statements is (are) true?

Which of the following is not true for a random variable X that is uniformly distributed over the interval $a \leq x \leq b$ ?

Given a binomial distribution with n trials and probability p of a success on any trial, a conventional rule of thumb is that the normal distribution will provide an adequate approximation of the binomial distribution if:

A random variable X is normally distributed with a mean of 150 and a variance of 25. Given that X = 120, its corresponding z-score is 6.0.

Which of the following distributions is appropriate to measure the length of time between arrivals at a grocery checkout counter?

In the normal distribution, the flatter the curve, the larger the standard deviation

In the exponential distribution, the value of x can be any of an infinite number of values in the given range.

Given that Z is a standard normal variable, the value z for which P(Z $\leq$ z) = 0.6736 is:

If the random variable X is uniformly distributed between 40 and 60, then P(35 $\le$ X $\le$ 45) is:

The height of the function for a uniform probability density function f(x):

The probability density function f(x) for a uniform random variable X defined over the interval [1, 11] is: