Question

You may need to use the appropriate appendix table or technology to answer this question.

A survey found that 91% of Americans believe that texting while driving should be outlawed.

(a)

For a sample of 10 Americans, what is the probability that at least 8 say that they believe texting while driving should be outlawed? Use the binomial distribution probability function discussed in Section 5.5 to answer this question. (Round your answer to four decimal places.)

(b)

For a sample of 100 Americans, what is the probability that at least 85 say that they believe texting while driving should be outlawed? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

(c)

As the number of trials in a binomial distribution application becomes large, what is the advantage of using the normal approximation of the binomial distribution to compute probabilities?

The advantage would be that using the normal probability distribution to approximate the binomial probabilities increases the number of calculations.The advantage would be that using the the normal probability distribution to approximate the binomial probabilities reduces the number of calculations.    The advantage would be that using the normal probability distribution to approximate the binomial probabilities makes the calculations less accurate.The advantage would be that using the normal probability distribution to approximate the binomial probabilities makes the calculations more accurate.

(d)

When the number of trials for a binominal distribution application becomes large, would developers of statistical software packages prefer to use the binomial distribution probability function shown in Section 5.5 or the normal approximation of the binomial distribution discussed in Section 6.3? Explain.

Answer 1

a) Let X denote number of Americans say that they believe texting while driving should be outlawed Sample size, n=10 Population proportion, p-91%-0.91 Here, X ~ Binom ( n = 10, p = 0.91 The binomial distribution probability function of X can be written as, 10 (0.91)*(1-0.91 10-х 10 0.91)" (0.09 x)( 10-х ) , x-0,1,2, ,10 Calculate probability that at least 8 say that they believe texting while driving should be outlawed. P(X28)-P(x-8)+P(X-9)+P(X-10) 10 0.91) 0.09) 10-8 (10 10-9 (0.91) (0.09109 10 10 10/0.91) (0.09)1o-0 0.1714+0.3851+0.3894 | 0.9459 b) Suppose sample size be, n-100 Calculate the probability that at least 85 say that they believe texting while driving should be outlawed, using normal approximation.

Let Xrepresent number of Americans say that they believe texting while driving should be outlawed, in a sample of 100 Americans X ~ Binom (n-100, р-091 Use Normal approximation of binomial distribution to find the required probability First calculate mean and standard deviation. np 100x0.91-91 σー、/np(1-p)イ100x0.91x(1-0.91)= 2.861818 The required probability is, P(X 2 85) P(X 85-0.5)Continuity correction) P(X>84.5) ơ 2.861818 P(Z>-2.27) - P(Z <2.27) NORMSDIST (227) Use z-table or 0.9884 Excel function Therefore, probability that at least 85 say that they believe texting while driving should be outlawed is 0.9884 c) When the number of trails in a binomial distribution becomes large, then calculation becomes complicated. In that case we use normal approximation, that gives almost same result

Correct option The advantage would be that using the normal probability distribution to approximate the binomial probabilities reduces the number of calculations d) They would use the Normal approximation of the binomial distribution discussed in Section 6.3