Question

According to a survey, 60% of adults believe that all college stu- dents should be required to perform a specified number of hours of community service to graduate. Assume that this percentage is true for the current population of adults.

a. Find the probability that the number of adults in a random sample of 12 who hold this view is
i. exactly 8 (use the appropriate formula)
ii. at least 6 (use the appropriate table from Appendix B)
iii. less than 4 (use the appropriate table from Appendix B)
b. Let x be the number of adults in a random sample of 12 who believe that all college students should be required to perform a specified number of hours of community service to gradu- ate. Using the appropriate table from Appendix B, write the probability distribution of x. Find the mean and standard deviation of x.

Answer 1

The table isnt attached, However, using formula we can obtain the result.

Answer:

0.2128 ; 0.8418 ; 0.015316

Explanation:

Using binomial probability formula :

P(x = x) = nCr * p^x * (1 - p)^(n-x)

p = 60% = 0.6

n = sample size = 12

Probability of :

i. exactly 8

P(x = 8) = 12C8 * 0.6^8 * 0.4^4

495 * 0.01679616 * 0.0256 = 0.2128

ii. at least 6

P(x ≥ 6) = p(6) + p(7) +... + p(12)

Using calculator to save computation time :

P(x ≥ 6) = 0.8418 (binomial probability calculator)

iii. less than 4

P( x < 4) = p(3) + p(2) + p(1) + p(0)

P( x < 4) = 0.0125 + 0.0025 + 0.0003 + 0.000016

= 0.015316