Question

in a recent poll, the gallup organization found that 45% of adult americans believe that the overall state of moral values in the united states is poor. if a survey of a random sample of 20 adults in this country is conducted in which they are asked to disclose their feelings on the overall state of moral values, complete parts (a) through (g).
the probability that exactly 11 of those surveyed feel the state of morals is poor is 0.1185
(round to four decimal places as needed.)
interpret the results.
in 100 trials of this experiment, we expect about 12 to result in exactly 11 adults who feel the state of morals is poor.
(round to the nearest whole number as needed.)
(d) using the binomial distribution, find and interpret the probability that no more than 5 of those surveyed feel the state of morals is poor.
the probability that no more than 5 of those surveyed feel the state of morals is poor is 0.0553
(round to four decimal places as needed.)
interpret the results.
in 100 trials of this experiment, we expect about □ to result in no more than 5 adults who feel the state of morals is poor.
(round to the nearest whole number as needed.)

Explanation:

Step1: Understand the concept of expected value in binomial distribution

The expected number of trials with a certain outcome is calculated by multiplying the total number of trials by the probability of that outcome.

Step2: Calculate the expected number of trials

We know the probability \(P(X\leq5) = 0.0553\) and the total number of trials \(n = 100\). The formula for the expected number \(E\) is \(E=n\times P\).
Substitute \(n = 100\) and \(P=0.0553\) into the formula: \(E = 100\times0.0553\).

Step3: Round the result

\(100\times0.0553=5.53\). Rounding \(5.53\) to the nearest whole number gives \(6\).

Answer:

In 100 trials of this experiment, we expect about \(6\) to result in no more than 5 adults who feel the state of morals is poor.