Exam 5: Discrete Probability Distributions

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Spinning a roulette wheel 9 times, keeping track of the occurrences of a winning number of "16."

Describe the differences in the Poisson and the binomial distribution.

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 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 certain rare form of cancer occurs in 37 children in a million, so its probability is 0.000037. In the city of Normalville there are 74,090 children. A Poisson distribution will be used to Approximate the probability that the number of cases of the disease in Normalville children is More than 2. Find the mean of the appropriate Poisson distribution (the mean number of cases In groups of 74,090 children).

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. Does the table describe a probability distribution? Why or why not? ( ) 0 0.674 1 0.280 2 0.044 3 0.003 4 0+

Use the given values of n=93 and p=0.24 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.

State the requirements to use the Poisson distribution as an approximation to the binomial distribution, including the mean for the Poisson distribution as an approximation to the binomial.

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+

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. ( ) 0 0.1296 1 0.3456 2 0.3456 3 0.1536 4 0.0256

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

Use the given values of n=1205 and p=0.98 to find the minimum value that is not significantly low, $\mu - 2 \sigma \text {, }$ 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.

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

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

The probability that a call received by a certain switchboard will be a wrong number is 0.02. Use the Poisson distribution to approximate the probability that among 150 calls received By the switchboard, there are at least two wrong numbers. Round your answer to four Decimal places.

In a magazine survey, 427 women are randomly selected without replacement and each woman is asked what she purchases online. Responses consist of whether clothing was identified. Determine whether the given procedure results in a distribution that is either binomial or can be treated as binomial. If not binomial, identify at least one requirement that is not satisfied.

In a certain town, 22 % of voters favor a given ballot measure. For groups of 21 voters, find the variance for the number who favor the measure.