To obtain: The probability that at most 80 drivers will say yes. Given info: The number of drivers selected in the United States is 200 and the drivers said yes for the given question is 0.47.

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To obtain: The probability that at most 80 drivers will say yes.  Given info:  The number of drivers selected in the United States is 200 and the drivers said yes for the given question is 0.47.

Nathaniel Kramer · Accepted Answer

Calculation: The drivers said yes for the given question p is 0.47. The adults said no for the given question q is 0.53. The requirements to check whether the normal distribution can be used for approximate the distribution of x, the binomial random variable are np≥5 and nq≥5. That is, Condition 1: np≥5 Condition 2: nq≥5 Condition 1: np≥5 Substitute 200 for n and 0.47 for p in the np. np=200×0.47 =94 &amp;gt;5 Thus, the given requirement np(=94)≥5 is satisfied. Condition 2: nq≥5 Substitute 200 for n and 0.53 for q in the nq. nq=200×0.53 =106 &amp;gt;5 Thus, the given requirement nq(=106)≥5 is satisfied. Since the requirements that np≥5 and nq≥5 both are satisfied. Thus, the normal distribution can be used to approximate the binomial distribution. That is, the probability from a binomial probability distribution can be approximated by using normal distribution with the parameters are, μ−np and σ=npq. The value of mean and standard deviation is, μ=200×0.47 =94 σ=200×0.47×0.53 =49.82 =7.058 Here, at most 80 drivers will say yes represents the binomial random variable x is more than 30. Continuity correction: If the binomial probability represents &quot;at more c&quot; then the normal probability is P(x&amp;lt;c+0.5) for any number c. By using continuity correction, the value 0.5 is added to the value of 80. That is, c=80 P(x≤80)=P(x&amp;lt;80+0.5) =P(x&amp;lt;80.5) Here, P(x&amp;lt;80.5) represents the area to the left of 80.5. The formula to convert the x value into z score is, z=x−μσ Substitute 80.5 for x, 94 for μ and 7.058 for σ z=80.5−947.058 =−13.57.058 NKS =−1.91 The probability that at most 80 drivers will say yes is obtained by finding area to the left of -1.91. Use Table 4: Standard normal distribution to find the area to the left of -1.91. Procedure: - Locate -1.9 in the left column of the Table 4. - Obtain the value in the corresponding row below 0.01. That is, P(z&amp;lt;−1.91)=0.0281 Thus, the probability that at most 80 drivers will say yes is 0.0281.

To obtain: The probability that at most 80 drivers will

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