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 (c) below.
click the icon to view the table.
a. find the probability of getting exactly 6 girls in 8 births.117 (type an integer or a decimal. do not round.)
b. find the probability of getting 6 or more girls in 8 births.142 (type an integer or a decimal. do not round.)
c. which probability is relevant for determining whether 6 is a significantly high number of girls in 8 births: the result from part (a) or part (b)?
a. the result from part b, since it is the probability of the given or more extreme result.
b. the result from part a, since it less than the probability of the given or more extreme result.
c. the result from part b, since it is the complement of the result of part a.
d. the result from part a, since it is the exact probability being asked.

Explanation:

Step1: Find probability for part a

From the table, when \(x = 6\) (number of girls), \(P(x)=0.117\)

Step2: Find probability for part b

To find \(P(x\geq6)\), we sum \(P(6)+P(7)+P(8)\)
\(P(6) = 0.117\), \(P(7)=0.021\), \(P(8)=0.004\)
\(P(x\geq6)=0.117 + 0.021+0.004=0.142\)

Step3: Determine relevant result for part c

Since \(P(x = 6)=0.117\) is used to check if \(6\) is a significantly high number (by comparing with a significance level, say \(0.05\) if \(P(x\geq6)\) is considered. But for the relation between part (a) and (b) for determining if \(6\) is significant, \(P(x = 6)\) (result from part a) is relevant as it is the probability of the exact value \(x = 6\) which is part of the calculation for \(x\geq6\) (but in terms of exact - value vs cumulative, when checking if a single value is extreme, the probability of that exact value (from part a) is relevant in some significance - based interpretations (e.g., in a binomial distribution, if we want to check if \(x = 6\) is an extreme outcome, \(P(x = 6)\) along with probabilities of more extreme values is considered. But if we just consider the role of part (a) in relation to checking \(x = 6\) as a single value for significance (in a simple - minded way of looking at just the probability of the exact value)), the result from part (a) is relevant.

Answer:

a. \(0.117\)
b. \(0.142\)
c. A. The result from part b, since it is the probability of the given or more extreme result.