Binomial Random Variables Answers

Zoologists estimate that a randomly selected baby giraffe has a 32% chance of surviving to adulthood. Assume this estimate is correct. Suppose researchers select 100 baby giraffes at random to tag and monitor. Let X = the number that survive to adulthood. Which conditions for a binomial setting have been met for this scenario? Binary? Independent? Number of trials? Same probability?

Suppose you and a friend are playing a game that involves rolling a fair die. You roll the die and count how many times you must roll until you roll a 6. Which conditions for a binomial setting have been met for this scenario? Binary? Independent? Number of trials? Same probability?

The makers of a certain diet cola claim that its taste is identical to the full-calorie version. To test this claim, a researcher recruits 175 volunteers, has them drink samples of both colas from identical cups in a randomized order, and then asks them to identify which sample is the diet cola. If we assume that the volunteers truly cannot tell the difference, then the probability that they correctly identify the diet cola is 0.5. Let X = the number of volunteers who correctly identify the diet cola. Which conditions for a binomial setting have been met for this scenario? Binary? Independent? Number of trials? Same probability?

Shuffle a standard deck of 52 playing cards. Turn over the first 10 cards, one at a time. Record the number of black kings you observe.Have the conditions for a binomial setting been met for this scenario?

Zoologists estimate that a randomly selected baby giraffe has a 32% chance of surviving to adulthood. Assume this estimate is correct. Suppose researchers select 100 baby giraffes at random to tag and monitor. X, the number of these giraffes that survive to adulthood, is a binomial random variable. Calculate the mean and standard deviation of X. Round to 4 decimal places, when necessary. μx = σx =

The makers of a certain diet cola claim that its taste is identical to the full-calorie version. To test this claim, a researcher recruits 175 volunteers, has them drink samples of both colas from identical cups in a randomized order, and then asks them to identify which sample is the diet cola. If we assume that the volunteers truly cannot tell the difference, then the probability that they correctly identify the diet cola is 0.5. X = the number of volunteers who correctly identify the diet cola and is a binomial random variable. Calculate the mean and standard deviation of X. Round to 4 decimal places, when necessary. μx = σx =

A spinner has two colored regions — purple and orange — and is divided in such a way so that the probability that the spinner lands on purple is 0.9. Suppose we spin the spinner 12 times and let X = the number of times it lands in the purple region. Calculate the mean and standard deviation of X. Round to 4 decimal places, when necessary. μx = σx =

A spinner has two colored regions — purple and orange — and is divided in such a way so that the probability that the spinner lands on purple is 0.9. Suppose we spin the spinner 12 times and let X = the number of times it lands in the purple region.What is the shape of the probability histogram of X?

Zoologists estimate that a randomly selected baby giraffe has a 32% chance of surviving to adulthood. Assume this estimate is correct. Suppose researchers select 100 baby giraffes at random to tag and monitor. Let X = the number that survive to adulthood.What is the shape of the probability histogram of X?

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