Question

1. A candy company claims that 25% of the jelly beans in its spring mix are pink. Suppose that the candies are packaged at random in small bags containing about 300 jelly beans. A class of students opens several bags, counts the various colors of jelly beans, and calculates the proportion that are pink in each bag. Is it appropriate to use an approximate Normal model to describe the distribution of the proportion of pink jelly beans?

   		An approximate Normal model is appropriate: Randomization condition is satisfied: the 300 jelly beans in the bag are selected at random and can be considered representative of all jelly beans 10% condition is satisfied: the sample size, 300, is less than 10% of the population of all jelly beans. The Rule of Thumb is satisfied: np = 75 and nq = 225 are both greater than 10
   		An approximate Normal model is not appropriate because the population distribution is not Normal
   		An approximate Normal model is not appropriate because the 10% condition is not satisfied: the sample size, 300, is larger than 10% of the population of all jelly beans.
   		An approximate Normal model is not appropriate because the Rule of Thumb is not met: np and nq are not greater than 10.
   		An approximate Normal model is not appropriate because the randomization condition is not satisfied: the 300 jelly beans in the bag are not a simple random sample and cannot be considered representative of all jelly beans.

2 points

Question 4

1. In the previous question, what is the mean of the sampling distribution for the sample proportion of pink jelly beans in each bag of 300?

In the previous question, what is the standard deviation of the sampling distribution for the sample proportion of pink jelly beans in each bag of 300?

Answer 1

Solution:-

3)

An approximate Normal model is appropriate:

Randomization condition is satisfied: the 300 jelly beans in the bag are selected at random and can be considered representative of all jelly beans

10% condition is satisfied: the sample size, 300, is less than 10% of the population of all jelly beans.

The Rule of Thumb is satisfied: np = 75 and nq = 225 are both greater than 10

4) The mean of the sampling distribution for the sample proportion of pink jelly beans in each bag of 300 is 0.25.

The standard deviation of the sampling distribution for the sample proportion of pink jelly beans in each bag of 300 is 0.025 .