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Exam 7: Continuous Probability Distributions

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Question 21

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If we ____________________ the normal curve,we express the original x values in terms of their number of standard deviations away from the mean.

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Question 22

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The probability that any continuous random variable x will take on any specific value along an interval is ____________________.

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A continuous random variable x has the following probability density function: f(x)= 2e^-2x ,x ≥ 0 What is the distribution of the random variable x?

A continuous random variable x is normally distributed with a mean of 120 grams and a standard deviation of 30 grams.Convert x = 106 into its corresponding z-score.

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 miss the net on a given night?

Which of the following is not a correct statement?

Any normal distribution is a symmetrical,bell-shaped curve,with mean $\mu$ = 0.0 and standard deviation $\text { ? }$ = 1.0.

For a normal curve,if the mean is 20 minutes and the standard deviation is 5 minutes,then the area between 22 and 25 minutes is:

Using the standard normal table,the total area between z = -0.75 and z = 1.21 is:

An elementary school teacher learned that 40 percent of school age children have at least 3 cavities.The teacher has 30 students in his class.What is the probability that 10 students from this class have at least 3 cavities?

Find the z-score that determines that the area to the left of z is 0.9292.

The mean of the exponential distribution equals the mean of the Poisson distribution only when the former distribution has a mean equals:

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(x ≥ 15).

Although the binomial distribution is discrete and the normal distribution is continuous,the normal distribution is a good approximation to the binomial whenever both ____________________ and ____________________ are ≥ 5,where n = number of trials,and $\pi$ = the probability of success in any given trial,are the parameters of the binomial distribution.

The recent average starting salary for new college graduates in computer information systems is $47,500.Assume salaries are normally distributed with a standard deviation of $4,500.What is the probability of a new graduate receiving a salary between $45,000 and $50,000?

A continuous probability distribution represents a random variable:

Which of the following distributions is suitable to model the length of time that elapses before the first telephone call is received by a switchboard?

The average waiting time at the checkout counter for a large grocery chain is 2.45 minutes with a standard deviation of 24 seconds (0.40 minutes).Assume that the distribution of waiting time is normal.What proportion of the customers are served in between 1 minute and 2.5 minutes?

Determine P(-2.45 ≤ z ≤ 0),assuming a standard normal distribution.

A continuous random variable x is normally distributed with a mean of $250 and a standard deviation of $50.Find the z-score for x = 285.