In a recent survey, 60% of the community favored building a health center in their neighborhood. If 14 citizens are chosen, find the probability that exactly 5 of them favor the building of the health center.

Probability that exactly 5 of them favor the building of the health center is 0.0408.

Step-by-step explanation:

We are given that in a recent survey, 60% of the community favored building a health center in their neighborhood.

Also, 14 citizens are chosen.

The above situation can be represented through Binomial distribution;

where, n = number of trials (samples) taken = 14 citizens

         r = number of success = exactly 5

        p = probability of success which in our question is % of the community

              favored building a health center in their neighborhood, i.e; 60%

LET X = Number of citizens who favored building of the health center.

So, it means X ~

Now, Probability that exactly 5 of them favor the building of the health center is given by = P(X = 5)

        P(X = 5) =

                      =

                      = 0.0408

Therefore, Probability that exactly 5 of them favor the building of the health center is 0.0408.

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;

step-by-step explanation:

6