the timer be set so that only 1 in 1000 cans will be underweight? g. Every day t

Question

the timer be set so that only 1 in 1000 cans will be underweight? g. Every day the company produces 10,000 cans. The government inspects 10 randomly chosen cans each day. If at least two are underweight, the company is fined $10,000. Given that = 12.05 ounces and 0.03 ounce, what is the probability that the company will be fined on a given day? Suppose that 53% of all registered voters prefer presidential candidate Smith to presidential candidate Jones. (You can substitute the names of the most recent presidential candidates.) a. In a random sample of 100 voters, what is the 26. probability that the sample will indicate that Smith will win the election (that is, there will be more votes in the sample for Smith)? b. In a random sample of 100 voters, what is the probability that the sample will indicate that Jones will win the election? c. In a random sample of 100 voters, what is the probability that the sample will indicate a dead heat (fifty-fifty)? d. In a random sample of 100 voters, what is the probability that between 40 and 60 (inclusive) voters will prefer Smith? Assume that, on average, 95% of all ticket holders show up for a flight. If a plane seats 200 people, how many tickets should be sold to make the chance of an overbooked flight as close as possible to 5%? 27. 28. Suppose that 55% of all people prefer Coke to Pepsi. We randomly choose 500 people and ask them if they prefer Coke to Pepsi. What is the probability that our

Explanation / Answer

Question 2.

Pr(Smith as prefer candidate) = 0.53

(a) Expected number of voters will vote for smith = 100 * 0.53 = 53

standard deviation of muber of voters for smith in a random sample of 100 = sqrt(0.53 * 0.47 * 100) = 4.99

so Here we have to know that in the sample smith will get more than 50 votes.

Pr(X > 50 ) = BIN (X > 50 ; 100 ; 0.53)

But as we approximate binomial to normal with continuity correction.

BIN (X > 50 ; 100 ; 0.53) = NORM (X > 50.5 ; 53 ; 4.99)

Z = (50.5 - 53)/ 4.99 = -0.50

so Pr(X > 50 ) = Pr(Z > -0.50) = 1- Pr(Z < -0.50) = 1 - 0.3085 = 0.6915

(b) Here Jones will win the election if smith will get less than 50 votes in the sample.

so Pr(X < 50) = BIN (X > 50 ; 100 ; 0.53)

approximate binomial to normal with continuity correction.

BIN (X < 50 ; 100 ; 0.53) = NORM (X < 49.5 ; 53 ; 4.99)

Z = (49.5 - 53)/ 4.99 = -0.70

so Pr(X < 50 ) = Pr(Z < 0.70) = 0.2420

(c) Here probability that the both will get 50 votes.

Pr(X = 50) = BIN (X = 50; 100 ; 0.53)

by binomial calculator

Pr(X = 50) = BIN (X = 50; 100 ; 0.53) = 0.0665

or we can calculate it with the answer of (a) and (b)

Pr(X = 50) = 1 - Pr(X > 50) - Pr(X < 50) = 1 - 0.6915 - 0.2420 = 0.0665

(d Here we have to find

Pr(40 = < X =< 60) = Pr(X =< 60) - Pr(X =< 40) = NORM (X < 60.5 ; 53; 4.99) - NORM (X < 39.5 ; 53; 4.99)

Z2 = (60.5 - 53)/ 4.99 = 1.50

Z1 = (39.5 - 53)/ 4.99 = -2.71

so Pr(40 = < X =< 60) = Pr(Z < 1.50) - Pr( Z < -2.71) = 0.9332 - 0.0034 = 0.9298

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