Exam 5: Discrete Probability Distributions

The Acme Candy Company claims that 60% of the jawbreakers it produces weigh more than 0.4 ounces. Suppose that 800 jawbreakers are selected at random from the production lines. Would it be significant for this sample of 800 to contain 494 jawbreakers that weigh more than 0.4 ounces? Consider as significant any result that differs from the mean by more than 2 standard deviations. That is, significant values are either less than $\mu - 2 \sigma$ or greater than $\mu + 2 \sigma$

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p . Round your answer to the nearest hundredth. n=503 ; p=0.7

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Rolling a single die 26 times, keeping track of the numbers that are rolled.

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. ( ) 0 0.109 1 0.208 2 0.246 3 0.159 4 0.096 5 0.228

Find the standard deviation, $\sigma$ , for the binomial distribution with n=38 and p=0.4 .

The probability that a car will have a flat tire while driving through a certain tunnel is 0.00005. Use the Poisson distribution to approximate the probability that among 14,000 cars passing through this tunnel, exactly two will have a flat tire. Round your answer to four decimal Places.

In a survey sponsored by Coca-Cola, subjects aged 15-65 were asked what contributes most to their happiness. The table is based on their responses. Determine whether a probability distribution is given and two reasons why or why not. Contributes Most to Happiness ( ) Family 0.77 Friends 0.15 Work/Study 0.08 Leisure 0.08 Music 0.06 Sports 0.04

The accompanying table shows the probability distribution for x, the number that shows up when a loaded die is rolled. ( ) 1 0.14 2 0.16 3 0.12 4 0.14 5 0.13 6 0.31

Describe the differences in the Poisson and the binomial distribution

Assume that a procedure yields a binomial distribution with a trial repeated n=30 times. Use the binomial probability formula to find the probability of x=5 successes given the probability p=1/5 of success on a single trial. Round to three decimal places.

Based on a Comcast survey, there is a 0.8 probability that a randomly selected adult will watch prime-time TV live, instead of online, on DVR, etc. Assume that seven adults are randomly selected. Find the probability that fewer than three of the selected adults watch Prime-time live.

A die is rolled nine times and the number of times that two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the number of twos.

A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800 , would it be significant to get 634 consumers who recognize the Dull Computer Company name? Consider as significant any result that differs from the mean by more than 2 standard deviations. That is, significant values are either less than $\mu - 2 \sigma$ or greater than $\mu + 2 \sigma$

Use the given values of n=2112 , $p = \frac { 3 } { 4 }$ to find the minimum value that is not significantly low, $\mu - 2 \sigma$ and the maximum value that is not significantly high, $\mu + 2 \sigma$ Round your answer to the nearest hundredth unless otherwise noted.

An experiment consists of rolling a single die 12 times and the variable x is the number of times that the outcome is 6. Can the Poisson distribution be used to find the probability that the outcome of 6 occurs exactly 3 times, why or why not?

The following table describes the results of roadworthiness tests of Ford Focus cars that are three years old (based on data from the Department of Transportation). The random variable x represents the number of cars that failed among six that were tested for roadworthiness: ( ) 0 0.377 1 0.399 2 0.176 3 0.041 4 0.005 5 0+ 6 0+ Is the probability of getting three or more cars that fail among six cars tested significant, Determined by a cutoff value of 0.05?

A tennis player makes a successful first serve 51% of the time. If she serves 9 times, what is the probability that she gets exactly 3 successful first serves in? Assume that each serve is independent of the others.

Use the given values of n=1205 and p=0.98 to find the minimum value that is not significantly low, $\mu - 2 \sigma$ , and the maximum value that is not significantly high, $\mu + 2 \sigma$ Round your answer to the nearest hundredth unless otherwise noted.

The following table describes the results of roadworthiness tests of Ford Focus cars that are three years old (based on data from the Department of Transportation). The random variable x represents the number of cars that failed among six that were tested for roadworthiness: ( ) 0 0.377 1 0.399 2 0.176 3 0.041 4 0.005 5 0+ 6 0+ Find the probability of getting three or more cars that fail among six cars tested.

In the month preceding this day, the author's mother made 18 phone calls in 30 days. No calls were made on 17 days, 1 call was made on 8 days, and 2 calls were made on 5 days. Use the Poisson distribution to find the probability of no calls in a day. Based on this probability, how many of the 30 days are expected to have no calls?