Exam 5: Discrete Probability Distributions

Mars, Inc. claims that $20 \%$ of its M\&M plain candies are orange. A sample of 100 such candies is randomly selected. Find the mean and standard deviation for the number of orange candies in such groups of 100 .

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?

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 $\mu + 2 \sigma$

List the three methods for finding binomial probabilities in the table below, and then complete the table to discuss the advantages and disadvantages of each. Methods Advantage Disadvantage

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. $n = 38 ; p = 2 / 5$

On a multiple choice test with 17 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the number of Correct answers.

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 $\mu - 2 \sigma \text { or greater than } \mu + 2 \sigma \text {. }$

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.

Find the mean, $\mu$ , for the binomial distribution which has the stated values of $n$ and $p$ . Round answer to the nearest tenth. $n = 676 ; p = 0.7$

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.

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.

Based on a USA Today poll, assume that 10% of the population believes that college is no longer a good investment. Find the probability that among 16 randomly selected people, at least 1 believes that college is no longer a good investment.

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. $n = 503 ; p = 0.7$

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.

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 $\mu + 2 \sigma$

A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the Student will pass the test? Round to three decimal places.

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

Describe the Poisson distribution and give an example of a random variable with a Poisson distribution.

For the table shown below, the random variable x is the number of males with tinnitus (ringing ears)among four randomly selected males, based on a medical journal. Find the mean and standard deviation for the random variable x. Use the range rule of thumb to identify the range of values that are not significant for the number of males with tinnitus among four randomly selected males. Is getting three males with tinnitus among four randomly selected males a significantly high number? ( ) 0 0.674 1 0.280 2 0.044 3 0.003 4 0+