Answer :
Answer:
Step-by-step explanation:
Let x be a random variable representing the number of the members of a men’s club that wear black vests to their club meetings. This is a binomial distribution since the outcomes are two ways. It is either they wear black or red. The probability of success, p = 70/100 = 0.7
The probability of failure, q would be 1 - p = 1 - 0.7 = 0.3
a) Number of samples, n = 10
We want to determine P(x ≤ 8)
From the binomial distribution calculator,
P(x ≤ 8) = 0.851
Answer:
The probability that at least 8 of the vest worn will be black is 0.75490
Step-by-step explanation:
The parameters given are;
The percentage of black vest worn = 70%, p₀ = 0.7
Number of men in sample, n = 10
Required number of men who wore black = 8
Proportion of sample [tex]\hat p[/tex] = 8/10 = 0.8
The z score of a proportion is given by the relation;
[tex]z = \dfrac{\hat p - p_0}{\sqrt{\dfrac{p_0(1 - p_0)}{n} } }[/tex]
Plugging in the vales, we have;
[tex]z = \dfrac{0.8 - 0.7}{\sqrt{\dfrac{0.7(1 - 0.7)}{10} } } = 0.69[/tex]
From the z table we have probability = p(z < 0.69) = 0.75490
The probability that at least 8 of the vest worn will be black = 0.75490.