Respuesta :
Answer:
0.235
Step-by-step explanation:
Define S as
S = the event that a randomly selected adult in the U.S. approves of President Trump.
Define ~S as the negation of S, i.e.,
~S = the event that a randomly selected adult in the U.S. does not approve of President Trump
Then,
P(S) = 40% = 0.4
P(~S) = 1 - 0.4 = 0.6
35% of 50 = 0.35 * 50 = 17.5.
We want to compute:
P(a random selection of 50 adults has less than 17.5 of them approving of President Trump) =
P(17 of the 50 approve) + P(16 of the 50 approve) + P(15 of the 50 approve) + . . . + P(none of the 50 approve).
We approximately compute this by approximating the summation (which is from a binomial distribution) by a normal distribution with
mean = 0.4(50) = 20,
and
standard deviation = sqrt( .4 * .6 * 50) = sqrt( 12 ) = 3.464 rounded to the nearest 1000th.
So, for normal random variable X with mean = 20 and std = 3.464, the probability that we want is approximately equal to P(X < 17.5), where we note that X is a real random variable.
So, the Z value = (17.5 - 20)/3.464 = -0.722, rounded to the nearest 1000th.
Using the normal random variable online calculator, https://stattrek.com/online-calculator/normal.aspx,
we get that
P(z < -0.722) = 0.235, which is the answer to the question.
