Math 1342 Summer 2018-75121 Elementary Statistics: A Step-By-Step Approach, 9th

Question

Math 1342 Summer 2018-75121 Elementary Statistics: A Step-By-Step Approach, 9th Ed nect IMATH Hosted by ALEKS Corp Section 6.4 Homework Previous 234 56 Next Question 5 of 6 (1 point) 6.4 Section Exercise 10 of all 3-to 5-year old children, 56% are enrolled in school. If a sample of 500 such children is randomly selected, find the probability that at least 258 will be enrolled in so answer to 4 decimal places and round intermediatez-value calculations to 2 decimal places. Source: Statistical Abstract of the United States. P(x 2258)- As Li Sav Ass

Explanation / Answer

Mean = np = 500 * 0.56 = 280

Standard deviation = sqrt(npq) = sqrt(500*0.56*0.44) = 11.099

Since ? = 280 and ? = 11.099 we have:

P ( X > 258 ) = P ( X?? > 258?280 ) = P ( X?? / ? > 258?280 / 11.099)

Since Z = x?? / ? and 258?280 / 11.099 = ?1.98 we have:

P ( X > 258 ) = P ( Z > ?1.98 )

Use the standard normal table to conclude that:

P (Z > ?1.98) = 0.9761

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