Question

the accompanying table describes results from groups of 8 births from 8 different sets of parents. the random variable x represents the number of girls among 8 children. complete parts (a) through (d) below.
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a. find the probability of getting exactly 1 girl in 8 births.
0.019 (type an integer or a decimal. do not round.)
b. find the probability of getting 1 or fewer girls in 8 births.
0.023 (type an integer or a decimal. do not round.)
c. which probability is relevant for determining whether 1 is a significantly low number of girls in 8 births: the result from part (a) or part (b)?
a. since the probability of getting 1 girl is the result from part (a), this is the relevant probability.
b. since the probability of getting 0 girls is less likely than getting 1 girl, the result from part (a) is the relevant probability.
c. since the probability of getting more than 1 girl is the complement of the result from part (b), this is the relevant probability.
d. since getting 0 girls is an even lower number of girls than getting 1 girl, the result from part (b) is the relevant probability.

Explanation:

Step1: Understand the concept of significantly low

To determine if 1 is a significantly low number of girls, we consider the probability of getting 1 or fewer girls. This is because significantly low events have a low - probability of occurring, and including the probability of getting 0 girls (which is part of the "1 or fewer" case) gives a more comprehensive view of the likelihood of having a very low number of girls.

Step2: Analyze the options

Option A only considers the probability of getting exactly 1 girl, which doesn't account for the even lower number of 0 girls. Option B has an incorrect reasoning as it doesn't correctly link the probabilities. Option C is correct because the probability of getting 1 or fewer girls (from part b) gives the overall likelihood of having a number of girls that is 1 or less, which is relevant for determining if 1 is a significantly low number. Option D has an incorrect focus on just comparing 0 and 1 without considering the overall "1 or fewer" concept for significance.

Answer:

C. Since the probability of getting more than 1 girl is the complement of the result from part (b), this is the relevant probability.