According to a recent Harris Poll, 28% of Americans state that chocolate is thei

Question

According to a recent Harris Poll, 28% of Americans state that chocolate is their favorite flavor of ice cream. Suppose a simple random sample of size 100 is obtained and is asked if their favorite ice cream flavor is chocolate. Let X be the number of Americans who choose chocolate as their favorite ice cream flavor.

4. Verify that X is approximately a binomial random variable. (BINS)

5. Check the conditions for using a Normal approximation.

6. Estimate the probability that 31 or more of the sample answered that chocolate is their favorite ice cream flavor.

Explanation / Answer

Here p=0.28 nd n=100

4.

The binomial distribution describes the behavior of a count variable X if the following conditions apply:

a: The number of observations n is fixed. Here it is 100

b: Each observation is independent.Here choice of one person is going to be different and hence they are different.

c: Each observation represents one of two outcomes ("success" or "failure").. Here either they like or they don't.

d: The probability of "success" p is the same for each outcome.Here p is 0.28 and its same for all

As all the conitions satisfied we say its binomial distribution.

5. Now np=.28>10 and npq=20.16>10 so we can consider normal approximation

6. Now we need to find P(x>=31), using normal approximation and converting x to z we get z=31-mean/sd

Where mean=np=28 and sd=sqrt(npq)=4.49

So z=31-28/4.49=0.67

So P(x>=31)=P(z>=0.67)=0.5-P(0<z<0.67)=0.5-0.2486=0.2514

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