Question

1.) In a recent​ survey,66​% of the community favored building a police substation in their neighborhood. If 14 citizens are​ chosen, find the probability that exactly 5 of them favor the building of the police substation. Round the answer to the nearest thousandth.

a.) .357

b.) .660

c.) .015

d.) .216

2.) A coin is tossed. Find the probability that the result is heads.

a.) .5

b.) .1

c.) 1

d.) .9

3.) The mean SAT verbal score is 464 with a standard deviation of 90. Use the empirical rule to determine what percent of the scores lie between 284 and 554. Assume the data set has a bell-shaped distribution.

a.) 68%

b.) 83.9%

c.) 34%

d.) 81.5%

Please answer all three questions! Thank you!

Answer 1

Q.1) This is a direct application of the binomial distribution with n = 14 and p = 0.66

Here, X ~ Binomial ( n = 14, p = 0.66)

probability mass function of X is,

We want to find, P( X = 5)

Answer: c) 0.015

Q.2) If a coin is tossed then probability that the result is head is 1/2 = 0.5

Answer: a) 0.5

Q.3) mean = 464 and standard deviation = sd = 90

i) mean - sd = 464 - 90 = 374 and

mean + sd = 464 + 90 = 554

ii) mean - 2 * sd = 464 - (2 * 90) = 464 - 180 = 284 and

mean + 2 * sd = 464 + (2 * 90) = 464 + 180 = 644

According to empirical rule,

i) approximately 68% of the data fall within 1 standard deviations of the mean.

ii) approximately 95% of the data fall within 2 standard deviations of the mean.

Therefore,

95/2 = 47.5% of the scores lie between mean - 2 * sd = 284 to mean = 464

and 68/2 = 34% of the scores lie between mean = 464 and mean + sd = 554

Therefore, 47.5% + 34% = 81.5% of the scores lie between 284 and 554

Answer: d) 81.5%