A particular moth can infest avocado trees and potentially damage the avocado fruit. A farmer plans to investigate the number of damaged avocado fruit on moth-infested avocado trees of a certain variety. A recent article states that the population distribution of the number of damaged avocado fruit on moth-infested avocado trees of this variety is symmetric with mean of 6.4 and standard deviation of 1.9. Required:

Compare the shapes of the sampling distributions of the sample mean number of damaged avocado fruit for random samples of 6 moth-infested trees and for random samples of 90 moth-infested trees from the population. Explain your answer.

By the Central Limit Theorem, both distributions are normal, with mean of 6.4. For samples of size 6, the standard deviation of the the sampling distributions of the sample mean number of damaged avocado fruit is of 0.78, while for samples of 90, it is of 0.2.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

A recent article states that the population distribution of the number of damaged avocado fruit on moth-infested avocado trees of this variety is symmetric with mean of 6.4 and standard deviation of 1.9.

So normally distributed, with

Samples of 6:

This means that

The mean is the same.

Samples of 90:

This means that

The mean is the same.

By the Central Limit Theorem, both distributions are normal, with mean of 6.4. For samples of size 6, the standard deviation of the the sampling distributions of the sample mean number of damaged avocado fruit is of 0.78, while for samples of 90, it is of 0.2.

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.

need points to ask question

step-by-step explanation: