3. A recent news article stated that only 17% of college students between the ages of 18 to 24 years old voted in the last presidential election. Assuming the voting rate stays the same, what is the probability that from a random sample of 500 college students from a local university, at least 20% will vote in the next presidential election

3.67% probability that from a random sample of 500 college students from a local university, at least 20% will vote in the next presidential election

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

The standard deviation of the binomial distribution is:

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that , .

In this problem, we have that:

.

So

Assuming the voting rate stays the same, what is the probability that from a random sample of 500 college students from a local university, at least 20% will vote in the next presidential election

This is 1 subtracted by the pvalue of Z when X = 500*0.2 = 100. So

has a pvalue of 0.9633

1 - 0.9633 = 0.0367

3.67% probability that from a random sample of 500 college students from a local university, at least 20% will vote in the next presidential election

won't that be plagrisim thought?

step-by-step explanation:

step by step resolutions

1) n+n+1+n+2=51

3n+3=51

3n=48

n=16

the three numbers are 16, 17 and 18.

2) x+15=4x

3x=15

x=5

radha is now 5 years old

3) the two digits are x and y.

y=3x

(10x+y)+(10y+x)=88

y=3x

11x+11y=88

y=3x

x+y=8

x+3x=8

x=2

the original number can be either 28 or 82.

4) n+(n+2)+(n+4)=48

3n+6=48

3n=42

n=14

the numbers are 14, 16 and 18.

5) y=x+3

10y+x+10x+y=143

y=x+3

11x+11y=143

y=x+3

x+y=13

x+x+3=13

2x=10

x=5

the original number can be 57 or 75.

hope this !