Question

1. a group of biologists study a population of squirrels in order to estimate the probability that a squirrels food storage will survive through the winter. based on data gathered across several years, the biologists report that the probability a squirrel will successfully store its food is equal to 0.82. from this information, along with what you know about probability, which one of the following statements is correct?

a. because probabilities cannot be greater than 1 or negative, 0.82 is a legitimate probability.
b. because probabilities can only be 0.5 or smaller, 0.82 is not a legitimate probability.
c. because the number 0.82 was based on past data, it should be called a prediction instead of being called a probability.
d. because a probability of 0.82 is equivalent to a percentage of 82%, and because 82 is larger than 1, it is impossible for a probability to equal 0.82.
e. because the value 0.82 was calculated from a sample, it is a statistic and not a true probability.

Explanation:

• Probability values range between \(0\) and \(1\) (inclusive). A value of \(0.82\) is within this range, so it is a legitimate probability.
• Option B is wrong because probabilities can be greater than \(0.5\).
• Option C is wrong as probability can be based on past data (empirical probability).
• Option D is wrong because when converting probability to percentage (\(0.82\times100 = 82\%\)), the percentage value \(82\) is just a scaled - up version of the probability value \(0.82\) (which is within \(0 - 1\)).
• Option E is wrong. A statistic calculated from a sample can be used as an estimate of a probability.

Answer:

A. Because probabilities cannot be greater than 1 or negative, 0.82 is a legitimate probability.