Question

1) We know that the height of pepper plants at week 11 of growth is distributed normally with mean 100 cm and standard deviation 32 cm. We have 64 pepper plants in our greenhouse. Find the probability that the average height of our 64 plants will be more than 105 cm. You may assume that the 64 pepper plants are a random sample. (8 points)

Answer 1

Since the height of the plant is normally distributed hence Z statistic is applicable here to find the probabilty of 64 random plants .

Here n=64 which is also greater than 30 so Z statistic rule also satisfy here.

Now,

$Z=\frac{\bar{X}-\mu}{\frac{\sigma}{\sqrt{n}}}$

$\bar{X}=Sample.Mean$

$\sigma=Standard deviation$

n=Sample size

Putting all the values in the formula we get,

Z= 1.25

Hence

$P ( \bar{X}>105})=P(Z>1.25)$

P value above Z score is calculated by Z table shown below as 0.1057