1. Information on the occupational prestige scores for blacks and whites is pres

Question

1. Information on the occupational prestige scores for blacks and whites is presented in the following table. Whites: Mean: 45.03, StD: 13.93, N.1,100 Blacks: Mean: 40.83, STD: 13.07, N 195 a. What percentage of whites should have occupational prestige scores above 60? How many whites in the sample should occupational prestige scores above 60? b. What percentage of blacks should have occupational prestige scores above 60? How many blacks in the sample should occupational prestige scores above 60? c. What proportion of whites have prestige scores between 30 and 70? How many whites have prestige scores between 30 and 70? d. How many blacks in the sample should have occupational prestige scores between 30 and 60? 2. The Hate Crime Statistics Act of 1990 requires the attorney general to collect national data about crimes that manifest evidence of prejudice based on race, religion, sexual orientation, or ethnicity, including the crimes of murder and non-negligent manslaughter, forcible rape, aggravated assault, simple assault, intimidation, arson, and destruction, damage, or vandalism of property. The hate crime data collected in 2007 reveal, based on randomly selected sample of 300 incidents, that the mean number of victims of a particular type of hate crime was 1.28, with a standard deviation of 0.82. Assuming that the number of victims of was normally distributed, answer the following questions. a. What proportion of crime incidents had more than 2 victims? b. What is the probability that there was more than 1 victim in an incident? c. What proportion of crime incidents had fewer than 4 victims? 3. The National Collegiate Athletic Association (NCAA) has a public access database on each Division I sports team in the United States, which contains data on team-level academic progress rates (APRs), eligibility rates, and retention rates. The mean APR of 359 men's basketball teams for the 2010-2011 academic year was 950.35 ( based on a 1,000-point scale), with a standard deviation of 30.58. Assuming that the distribution of APRs for the teams is approximately normal, a. Would a team be at the upper quartile ( the top 25%) of the APR distribution with an APR score of 975? b. What APR score should a team have to be more successful than 75% of all the teams. c. What is the Z value for this score? 4. What is the value of the teams score for any standard normal distribution? What is the value of the standard deviation for any standard normal distribution? Explain why this is true for any standard normal distribution.

Explanation / Answer

1) Whites: Mean: 45.03, StD: 13.93, N.1,100 Blacks: Mean: 40.83, STD: 13.07, N 195

a) we need to find for white p(x>60)

For x = 60, z = (60 - 45.03) / 13.93 = 1.07

Hence P(x > 60) = P(z > 1.07) = [total area] - [area to the left of 1.07]

1 - [area to the left of 1.07]

now from the z table we will take the value of z score = 1.07

    = 1 - 0.8577 = 0.1423

therefore 0.1423*1000= 142.3 whites

b) for blacks p(x>60)

For x = 60, z = (60 - 40.83) / 13.07 = 1.46

Hence P(x > 60) = P(z > 1.46) = [total area] - [area to the left of 1.46]

1 - [area to the left of 1.46]

now from the z table we will take the value of z score = 1.46

    = 1 - 0.9279 = 0.0721

c) we need to find the whites p(30<x<70)

For x = 30 , z = (30 - 45.03) / 13.93 = -1.07 and for x = 70, z = (70 - 45.03) / 13.93 = 1.79

Hence P(30 < x < 70) = P(-1.07 < z < 1.79) = [area to the left of z = 1.79] - [area to the left of -1.07]

= 0.9633 - 0.1423 = 0.821

d)

For x = 30 , z = (30 - 40.83) / 13.07 = -0.82 and for x = 60, z = (60 - 40.83) /13.07 = 1.46

Hence P(30 < x < 60) = P(-0.82 < z < 1.46) = [area to the left of z = 1.46] - [area to the left of -0.82]

= 0.9279 - 0.2061 = 0.7218

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