Identifying Binomial Distributions. In Exercises 5–12, determine whether the given procedure results in a binomial distribution (or a distribution that can be treated as binomial). For those that are not binomial, identify at least one requirement that is not satisfied.

Clinical Trial of YSORT The YSORT method of gender selection, developed by the Genetics & IVF Institute, was designed to increase the likelihood that a baby will be a boy. When 291 couples used the YSORT method and gave birth to 291 babies, the weights of the babies were recorded.

Short Answer

Expert verified

The given situation cannot be approximated using the binomial distribution as the baby's weight has more than two possible outcomes.

Step by step solution

01

Given information

Out of 291 couples who used the YSORT method to give birth to 291 babies, the weights of the 291 babies are recorded.

02

Assumptions of binomial distribution

The following assumptions of the binomial distribution should be satisfied:

  • The procedure should have a fixed number of trials.
  • The trials should be independent.
  • Each trial should have outcomes that are of exactly two kinds: success and failure.
  • The probability of success should be the same for all the trials.
03

Violation of an assumption

Out of the given set of assumptions required for a procedure to follow the binomial distribution,one such assumption is that the outcomes of the event whose probability is to be computed should be of exactly two kinds.

One outcome is considered as the success, and the remaining outcome is considered as the failure.

Here, the weight of a baby is recorded.

Weight can have more than two possible outcomes.

Therefore, the given situation cannot be modeled using the binomial distribution.

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Most popular questions from this chapter

a.The probability of 7 hurricanes in a year is equal to 0.140.

b. Thus, the expected number of years to have 7 hurricanes in a 55-year period is equal to 7.7 years.

c. The expected number of years that have 7 hurricanes is approximately equal to the actual number of years that have 7 hurricanes in a 55-year period.Since the expected and the actual values are approximately equal, the Poisson distribution works well here.

Ultimate Binomial Exercises! Exercises 37–40 involve finding binomial probabilities, finding parameters, and determining whether values are significantly high or low by using the range rule of thumb and probabilities.

Politics The County Clerk in Essex, New Jersey, was accused of cheating by not using randomness in assigning line positions on voting ballots. Among 41 different ballots, Democrats were assigned the top line 40 times. Assume that Democrats and Republicans are assigned the top line using a method of random selection so that they are equally likely to get that top line.

a. Use the range rule of thumb to identify the limits separating values that are significantly low and those that are significantly high. Based on the results, is the result of 40 top lines for Democrats significantly high?

b. Find the probability of exactly 40 top lines for Democrats

c. Find the probability of 40 or more top lines for Democrats.

d. Which probability is relevant for determining whether 40 top lines for Democrats is significantly high: the probability from part (b) or part (c)? Based on the relevant probability, is the result of 40 top lines for Democrats significantly high?

e. What do the results suggest about how the clerk met the requirement of assigning the line positions using a random method?

For 100 births, P(exactly 56 girls) = 0.0390 and P(56 or more girls) = 0.136. Is 56 girls in 100 births a significantly high number of girls? Which probability is relevant to answering that question?

In Exercises 21–24, assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an LG Smartphone survey).

If 20 adult smartphone users are randomly selected, find the probability that exactly 15 of them use their smartphones in meetings or classes.

Significance with Range Rule of Thumb. In Exercises 29 and 30, assume that different groups of couples use the XSORT method of gender selection and each couple gives birth to one baby. The XSORT method is designed to increase the likelihood that a baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5.

Gender Selection Assume that the groups consist of 36 couples.

a.Find the mean and standard deviation for the numbers of girls in groups of 36 births.

b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.

c. Is the result of 26 girls a result that is significantly high? What does it suggest about the effectiveness of the XSORT method?

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