Assignment 4a & 4b



Assignment 4a & 4b

Assignment 4a - Conducting Data Analysis

Q1 Consider a normal distribution with mean 20 and standard deviation SD=3. Find the probability that a measurement will be between 12 and 20.

First there needs to be a calculation of the number of standard deviations that lie away from the mean.

Z = (12-20)/3=2.67

Thus 12 lies 2.67 SD below the mean of 20.

From the Z calculator we get that the probability of a measurement falling between 12 and 20 is 0.4962 or 49.62%.

Q2 The distribution of weights of a large group of high school boys is normal with mean=120 pounds and SD=10 pounds.

About 25% of the boys will be over 130 pounds. True or False?  

We first need to calculate the number of standard deviations that lie above the mean.

Z = (130-120)/10

Thus 130 pounds lies 1 SD above the mean of 120 pounds.

From the Z calculator we get that the probability of a measurement falling over 130 pounds is 0.1587 or 15.87%. This suggests that the statement of 25% of the boys will be over 130 pounds is False.

About 20% of the boys will be below 100 pounds. True or False? 

We first need to calculate the number of standard deviations that lie below the mean.

Z = (120-100)/10

Thus 100 pounds lies 2 SD below the mean of 120 pounds.

From the Z calculator we get that the probability of a measurement falling below 100 pounds is 0.0228 or 2.28%. This suggests that the statement of 20% of boys being below 100 pounds is False.

Half of the boys can be expected to weigh less than 120 pounds. True or False? 

Noticing that the value of 120 pounds is the mean of the study. The calculation should result in a z-score of 0.

Z = (120-120)/3

Thus 120 lies with 0 SD since it is the mean.

From the Z calculator we get that the probability of a measurement that lies on 120 pounds is 0.5 or 50%. This suggests that the statement of 50% of the boys having weight less than 120 pounds is True (Babbie 2010 p. 1-624).

Q3 The mean birth-weight for ALL the children born at a certain hospital is 112 oz and the standard deviation is 40 oz. Note: Please refer to your reading assignment in the background section. Use the Central Limit Theorem and the Z table.

Compute the probability that the mean birth-weight from a sample of 49 infants from the hospital will fall between 103 and 121 oz.

We first need to calculate the standard error of the mean by utilizing standard deviation of 40 oz with a sample of 49 infants.

M = 40/49)

The standard error of the mean is 5.71.

Next utilizing the standard error of the mean, calculate the interval of the Z-score.

(103-112)/5.71 = -1.58and (121-112)/5.71 = 1.58

Utilizing the two z-scores, probability distribution needs to be calculated as follows.

Z (-1.58) = p (1-0.4429)Z (1.58) = p (0.4429)

= p (0.5571)= p (0.4429)

The final probability is the difference found between the values.

p = (0.5571 - 0.4429)

The probability found of the mean birth-weight of ...