**Solution for the Following:** | A distribution has a standard deviation of σ=12. Find the z-score for each of the following locations in the distribution.
a. Above the mean by 3 points
b. Above the mean by 12 points.
c. Below the mean by 24 points
d. Below the mean by 18 points.
For a population with a mean of µ=100 and a standard deviation of σ =12,
a. Find the z-score for each of the following X values. X=106, X=115, X=130, X=91, X=88, X=64
b. Find the score (X value) that corresponds to each of the following z-scores. Z=-1.00, z =-0.50, z =2.00, z =0.75, z =1.50, z =-1.25
Find the z-score corresponding to a score of X=60 for each of the following distributions.
a. µ=50 and σ =20
b. µ=50 and σ =10
c. µ=50 and σ =5
d. µ=50 and σ =2
For a population with a standard deviation of σ =8, a score of X=44 corresponds to
z =-0.50. What is the population mean?
For a sample with a mean of µ= 45, a score of X=59 corresponds to z =2.00. What is the sample standard deviation?
For each of the following population, would a score of x =50 be considered a central score (near the middle of the distribution) or an extreme score (far out in the tail of the distribution)?
a. µ=45 and σ =10
b.µ=45 and σ =2
c.µ=90 and σ =20
d.µ=60 and σ =20
For each of the following, identify the exam score that should lead to the better grade, in each case, explain your answer.
a. A Score of x =56, on an exam with µ=50 and σ =4, or a score of x =60, on an exam with µ=50 and σ =20.
b. A Score of x =40, on an exam with µ=45 and σ =2, or a score of x =60, on an exam with µ=70 and σ =20
c. A Score of x =62, on an exam with µ=50 and σ =8, or a score of x =23, on an exam with µ=20 and σ =2.
What is sampling with replacement, and why is it used?
Find the z-score location of the vertical line that separates a normal distribution as described in each of the following.
For a normal distribution with a mean of µ=80 and a standard deviation of σ =20, find the proportion of the population corresponding to each of the following scores.
a. Scores greater than 85
b. Score less than 100
c. scores between 70 and 90.
IQ test scores are standardized to produce a normal distribution with a mean of µ=100 and a standard deviation of σ =15. Find the proportion of the population in each of the following IQ categories.
a. Genius or near genius: IQ over 140
b. Very superior intelligence: IQ from 120-140
c. Average or normal intelligence: IQ from 90-109
The distribution of sample means is not always a normal distribution. Under what circumstances will the distribution of sample means not be normal?
For a population with a mean of µ=60 and a standard deviation of σ =24, find the z-score corresponding to each of the following samples.
The population of IQ scores forms a normal distribution with a mean of µ=100 and a standard deviation of σ =15. What is the probability of obtaining a sample mean greater than M=105,
a. for a random sample of n=9 people?
b. for a random sample of n=36 people?
A population of scores forms a normal distribution with a mean of µ=40 and a standard deviation of σ =12.
a. What is the probability of randomly selecting a score less than X =34?
b. What is the probability of selecting a sample of n=9 scores with a mean of less than M=34?
c. What is the probability of selecting a sample of n=36 scores with a mean of less than M=34? |