A candy maker offers Child and Adult bags of jelly beans with different color mixes. The company claims that the Child mix has 3
0% red jelly beans, while the Adult mix contains 15% red jelly beans. Assume that the candy maker’s claim is true. Suppose we take a random sample of 50 jelly beans from the Child mix and a separate random sample of 100 jelly beans from the Adult mix. Let 
and 
be the sample proportions of red jelly beans from the Child and Adult mixes, respectively.
Find the probability that the proportion of red jelly beans in the Child sample is less than or equal to the proportion of red jelly beans in the Adult sample, assuming that the company’s claim is true.
Find the probability that the proportion of red jelly beans in the Child sample is less than or equal to the proportion of red jelly beans in the Adult sample, assuming that the company’s claim is true.
1 answer:
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Answer:
Mean $1060
Standard error $34.69
Step-by-step explanation:
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, which is also called standard error,
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Population:
Mean $1,060 and standard deviation $190.
Sampling distriution of samples of size 30:
Mean $1060
Standard deviation