Question

Gardening: A gardener buys a package of seeds. 80% of seeds of this type germinate. The Gardner plates 90 seeds. A=approximate the probability that fewer than 75 seeds germinate.x= the number of seeds germinate

Answer 1

Answer:

$0.7852$

Explanation:

The probability we want to calculate is:

$P(X\text{ < 75\rparen}$

Now, we use the normal approximation of the binomial distribution

That would be:

p = 0.8 (probability of germination) given as 80%

q = 1 - p = 0.2 (probability of no germination)

We have the mean as:

$mean\text{ = np = 90 }\times\text{ 0.8 = 72}$

We have the standard deviation as:

$SD\text{ = }\sqrt{npq}\text{ = }\sqrt{90\times0.8\times0.2}\text{ = 3.795}$

Now, let us get the value of z;

$\begin{gathered} z\text{ = }\frac{x-\text{ mean}}{SD} \\ \\ z\text{ = }\frac{75-72}{3.975}\text{ = 0.79} \end{gathered}$

Now, we use the standard normal distribution table

$P(z\text{ < 0.79\rparen = 0.7852}$