According to a poll on consumer behavior,36%of people say they will only conside

Question

According to a poll on consumer behavior,36%of people say they will only consider cars manufactured in their country when purchasing a new car. Suppose you select a random sample of 100 respondents. Complete parts (a) through (c) below.

a. What is the probability that the sample will have between30% and39% who say they will consider only cars manufactured by a company in their country when purchasing a new car?The probability is 0.6301.

(Round to four decimal places as needed.)

b. The probability is 70%that the sample will be contained within what symmetrical limits of the population percentage?The probability is70%

that the sample percentage will be contained above nothing% and below nothing%.

Explanation / Answer

a)

p = 0.36 , n = 100

P(0.3 < x < 0.39)
= P( ( 0.3 - 0.36) / sqrt(0.36 * (1 - 0.36) / 100) < z < (0.39 - 0.36) / sqrt(0.36 * (1 - 0.36) / 100))
= P(-1.25 < z < 0.625)

P(0.3 < x < 0.39) =P(-1.25 < z < 0.625) = 0.6284 by using standard normal table

b)

z value at 70% = -/+ 0.5244
SE = sqrt(p * ( 1- p)/n) = sqrt(0.36*0.64/100) = 0.048

as per central limit theorem,

pcap = p + z*SE = 0.3852
pcap = p - z*SE = 0.3348

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