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.
number of girls, x p(x)
0 0.004
1 0.017
2 0.114
3 0.204
4 0.322
5 0.204
a. find the probability of getting exactly 6 girls in 8 births.
(type an integer or a decimal. do not round.)
b. find the probability of getting 6 or more girls in 8 births.
(type an integer or a decimal. do not round.)
c. is 6 a significantly high number of girls in 8 births? why or why not? use 0.05 as the threshold for a significant event.
a. yes, since the appropriate probability is greater than 0.05, it is a significantly high number.
b. no, since the appropriate probability is less than 0.05, it is not a significantly high number.
c. no, since the appropriate probability is greater than 0.05, it is not a significantly high number.
d. yes, since the appropriate probability is less than 0.05, it is a significantly high number.

Explanation:

Step1: Find probability of exactly 6 girls

From the table, when \(x = 6\), \(P(x)=0.204\)

Step2: Find probability of 6 or more girls

\(P(X\geq6)=P(X = 6)+P(X = 7)+P(X = 8)\)
\(P(X = 6)=0.204\), \(P(X = 7)=0.322\), \(P(X = 8)=0.204\)
\(P(X\geq6)=0.204 + 0.322+0.204=0.73\)

Step3: Check significance for 6 girls in 8 births

A probability less than \(0.05\) is considered significant. Since \(P(X = 6)=0.204>0.05\), it is not significant. But for \(P(X\geq6) = 0.73>0.05\) (re - check based on problem's part c criteria)

Answer:

a. \(0.204\)
b. \(0.73\)
c. B. No, since the appropriate probability is greater than \(0.05\), it is not a significantly high number.