Exam 8: Probability Distributions and Statistics

On the average, a student takes 100 words/minute midway through an advanced court reporting course at the American Institute of Court Reporting. Assuming that the dictation speeds of the students are normally distributed and that the standard deviation is 20 words/minute, what is the probability that a student randomly selected from the course can take dictation at a speed. Round your answers to four decimal places, if necessary.

Let X denote the random variable that gives the sum of the faces that fall uppermost when two fair dice are cast. Find P ( X = 5 ). ​

Use the formula to determine the probability to four decimal places of the given event. The probability of exactly no successes in five trials of a binomial experiment in which

The medical records of infants delivered at Kaiser Memorial Hospital show that the infants' lengths at birth (in inches) are normally distributed with a mean 25 and a standard deviation of 2.5. Find the probability that an infant selected at random from among those delivered at the hospital measures less than 19 in. ​

How many times must a person toss a coin if the chances of obtaining at least one head are 91% or better? ​

The probability that an airplane engine will fail in a transcontinental flight is 0.002. Assuming that engine failures are independent of each other, what is the probability that a four-engine plane will experience exactly two engine failure?

The histograms represent the probability distributions of the random variables X and Y. Determine by inspection which probability distribution has the larger variance.

Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve. Round your answer to four decimal places, if necessary. P ( Z > 1.16 ) = __________

Find the value of the probability of the standard normal variable Z corresponding to this area. P ( 0.63 < Z < 2.01 )

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The area of a histogram associated with a probability distribution is a number between 0 and 1.

Find for the given values of n, x, and p. Round the answer to four decimal places, if necessary. n = 5, x = 3, p = 0.7 = __________

The mean annual starting salary of a new graduate in a certain profession is $43,000 with a standard deviation of $500. What is the probability that the starting salary of a new graduate in this profession will be between $39,500 and $46,500?

After the private screening of a new television pilot, audience members were asked to rate the new show on a scale of 1 to 10 (10 being the highest rating). From a group of 140 people, the accompanying responses were obtained. ​ ​ Let the random variable X denote the rating given to the show by a randomly chosen audience member. Find the probability distribution associated with these data. Round answer to the nearest thousandth.

Use the formula to determine the probability to four decimal places of the given event. The probability of exactly no failures in four trials of a binomial experiment in which

A woman purchased a $10,000, 1-year term-life insurance policy for $150. Assuming that the probability that she will live another year is 0.993, find the company's expected gain.

Find the variance of the probability distribution for the histogram. Give your answer to two decimal places, if necessary. ​ ​ Var ( X ) = __________

Use the appropriate normal distribution to approximate the resulting binomial distribution. Round your answers to four decimal places. A fair coin is tossed 20 times. What is the probability of obtaining fewer than 8 heads? __________ What is the probability of obtaining more than 8 heads? __________ What is the probability of obtaining between 6 and 11 heads inclusive? __________

The probability that a fuse produced by a certain manufacturing process will be defective is . Is it correct to infer from this statement that there is at most 1 defective fuse in each lot of 49 produced by this process?

The probability that a fuse produced by a certain manufacturing process will be defective is . Is it correct to infer from this statement that there is at most 1 defective fuse in each lot of 56 produced by this process? Justify your answer.

Find the expected value of a random variable X having the following probability distribution. Give your answer to two decimal places, if necessary. E (X) = __________