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

`0.7852`

Step-by-step 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 }*\text{ 0.8 = 72}`

We have the standard deviation as:

`SD\text{ = }√(npq)\text{ = }√(90*0.8*0.2)\text{ = 3.795}`

Now, let us get the value of z;

`\begin{gathered} z\text{ = }\frac{x-\text{ mean}}{SD} \\ \\ z\text{ = }(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}`