Answer:
P(X is greater than 30) = 0.06
Step-by-step explanation:
Given that:
Sample proportion (p) = 0.5
Sample size = 30
The Binomial can be approximated to normal with:
[tex]\mu = np = 50 \times 0.5 \\ \\ \mu= 25[/tex]
[tex]\sigma = \sqrt{np(1-p) } \\ \\ \sigma = \sqrt{50 \times (0.5)(1-0.5) } \\ \\ \sigma = 3.536[/tex]
To find:
P(X> 30)
So far we are approximating a discrete Binomial distribution using the continuous normal distribution. 30 lies between 29.5 and 30.5
Normal distribution:
x = 30.5, [tex]\mu[/tex] = 25, [tex]\sigma[/tex] = 3.536
Using the z test statistics;
[tex]z = \dfrac{x - \mu}{\sigma}[/tex]
[tex]z = \dfrac{30.5 - 25}{3.536}[/tex]
[tex]z = \dfrac{5.5}{3.536}[/tex]
z = 1.555
The p-value for P(X>30) = P(Z > 1.555)
The p-value for P(X>30) = 1 - P (Z< 1.555)
From the z tables;
P(X> 30) = 1 - 0.9400
Thus;
P(X is greater than 30) = 0.06
