7, Find the critical value Zo, for -0.02. Round your answer to 2 decimal places.

Question

7, Find the critical value Zo, for -0.02. Round your answer to 2 decimal places. According to Statistic Brain, 14% of Americans (all ages) have at least one tattoo. Suppose 80 Americans are randomly selected. 8, a) Verify that it is appropriate to use the normal approximation to the binomial distribution in this case. You must show calculations to receive full credit b) Find the mean number of people in groups of 80 Americans who have at least one tattoo. Find the standard deviation of the number of people in groups of 80 Americans who have at least one tattoo. c) d) Use the normal approximation to the binomial distribution to estimate the probability that at least 15 out of 80 randomly chosen Americans have at least one tattoo. Write your answer as a decimal rounded to 4 decimal places. You must show your calculator function and input (including the continuity correction) to receive full credit.

Explanation / Answer

7)

P(Z > z*) = 0.02

z* = 2.054

8)  

n = 80 , p= 0.14

a) np = 80*0.14 = 11.2 > 5

npq = 68.2 > 5

hence normal approximation can be done

b)

mean = E(X) = np = 11.2

c) sd (X) =sqrt(npq) = sqrt(68.8) = 8.294577

d)

P(X >= 15)

= P( X > 14.5)

= P (Z >( 14.5 - 11.2)/8.294577)

= P(Z> 0.397850)

= 0.3454

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