Suppose a population is normally distributed (and you are a member of the popula

Question

Suppose a population is normally distributed (and you are a member of the population)

If you have a standard score of Z = 2, what percentage of the population has scores greater than you?

If you have a standard score of Z = - 2, what percentage of the population has scores greater than you?

If you have a standard score of Z = 1, what percentage of the population has scores less than you?

If you have a standard score of Z = 1, what percentage of the population has scores farther away from the population mean (in either direction) than you?

If you have a standard score of Z = -1.7, what percentage of the population has scores farther away from the population mean (in either direction) than you?

If you have a standard score of Z = -1.7, what percentage of the population has scores greater than you?

Explanation / Answer

1. Given Z follows a standard normal distribution,

a. P(Z > 2) = 2.275%

b. P(Z > -2) = 97.725%

c. P(Z < 1) = 84.134%

d. P( |Z| > 1) = P(Z<-1) + P(Z>1) = 15.866% + 15.866% = 31.732%

e. P( |Z| > 1.7) = P(Z<-1.7) + P(Z>1.7) = 4.4565% + 4.4565% = 8.913%

f. P(Z > -1.7) = 1 - P(Z<-1.7) = 100% - 4.4565% = 95.5435%

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.