Answer:
a
[tex]S.E = 0.05[/tex]
b
[tex]P(P > 0.75) = 0.0013499[/tex]
Step-by-step explanation:
From the question we are told that
The population [tex]p = 0.60[/tex]
The sample size is [tex]n = 96[/tex]
The sample proportion is [tex]\r p = 0.75[/tex]
Generally the standard error is mathematically represented as
[tex]S.E = \sqrt{ \frac{p(1-p)}{n } }[/tex]
substituting values
[tex]S.E = \sqrt{ \frac{0.60 (1-0.60 )}{96 } }[/tex]
[tex]S.E = 0.05[/tex]
The probability that more than 75% of consumers will indicate they like the drink is mathematically represented as
[tex]P(P > 0.75) = P(\frac{\r P - p }{\sqrt{\frac{p(1-p)}{n} } } > \frac{\r p - p }{\sqrt{\frac{p(1-p)}{n} } } )[/tex]
The z-score is evaluated as
[tex]z = \frac{\r p - p }{\sqrt{\frac{p(1-p)}{n} } }[/tex]
So
[tex]P(P > 0.75) = P(Z > \frac{0.75 - 0.60 }{0.05} )[/tex]
[tex]P(P > 0.75) = P(Z > 3)[/tex]
[tex]P(P > 0.75) = 0.0013499[/tex]
This value above is obtained from the z-table
