Question

A candy company claims that its jelly bean mix contains 23% blue jelly beans. Suppose that the candies are packaged at random in small bags containing about 350 jelly beans. Find the mean of the proportion of blue jelly beans in a bag.

Answer 1

Answer:

For this case we can use the normal approximation since w satisfy these two conditions:

1) np= 350*0.23= 80.5>10

2) n(1-p) =350*(1-0.23)= 269.5>10

So then the mean for the real proportions is given by:

$\mu_{p}= 0.23$

And the expected number of blu ebelly jeans are:

$E(X) = np= 350*0.23= 80.5$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest "number of blue jelly beans in a sample of 350", on this case we now that:

$X \sim Binom(n=350, p=0.23)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

For this case we can use the normal approximation since w satisfy these two conditions:

1) np= 350*0.23= 80.5>10

2) n(1-p) =350*(1-0.23)= 269.5>10

So then the mean for the real proportions is given by:

$\mu_{p}= 0.23$

And the expected number of blu ebelly jeans are:

$E(X) = np= 350*0.23= 80.5$

Answer 2

The mean of the proportion of blue jelly beans in a bag is $\rm \mu_p = 0.23$

Given :

• A candy company claims that its jelly bean mix contains 23% blue jelly beans.
• Suppose that the candies are packaged at random in small bags containing about 350 jelly beans.

It is given that the sample size is 350. The normal approximation can be used because 'w' satisfies the below conditions, that is:

$\rm np = 350\times 0.23 = 80.5 > 10$

$\rm n(1-p) = 350\times (1-0.23) = 269.5> 10$

Therefore, the mean of the proportion of blue jelly beans in a bag is :

$\rm \mu_p = 0.23$

So, the expected number of blue jelly beans are given by:

E(X) = np = 80.5

For more information, refer to the link given below:

https://brainly.com/question/23017717