Question

An investigation of the ability of a hybrid tomato plant to produce a certain protein found that the amount x of the protein produced in the plant had a mean of 109.9109.9 micrograms per gram of fresh weight with a standard deviation of 8.18.1. consider a random sample of n equals 60n=60 hybrid tomato plants and let x overbarx represent the sample mean amount of the protein produced. would it be expected to observe a value of x overbarx less than 107107 micrograms per gram of fresh​ weight? explain. consider an event with a probability less than 0.05 unlikely.

Answer 1

This is a Question of Statistics and an application of standard normal distribution.

Average amount(Mean) of protein produced by the plant = 109.9 
Standard Deviation = 8.1

Size of the sample = 60
Average amount of  protein for the sample is the same as that of population.So average amount of protein for the sample = 109.9
Standard Deviation of the sample = (Population Standard Deviation) divided by (square root of sample size)
So sample standard deviation = $\frac{8.1}{ \sqrt{60} }=1.046$

So, we are to find the probability of amount of protein being produced less than 107 for mean 109.9 and standard deviation 1.046.

First we convert this value to z score.

Z-score = $\frac{107-109.9}{1.046}= -2.77$

Using z-table, converting this z score to probability we get:

Probability of mean being less than 107 = 0.0028

Since the probability of mean being less than 107 is less than 0.05. This event is highly unlikely.