PROBABILITY
4.11.3.2 First Homework on Standardization of Variables
(Module 11 Topic 3 HW1)
Date Due:
Student’s Name:
In these exercises, we speak of “natural units” such as Fahrenheight degrees or feet or kilograms and “standardized units” or stds. Where we may
use x to represent the value of a random variable expressed in natural units,
we will use z as the corresponding value expressed in standardized units. The
conversion between the two values is accomplished by the following formulas:
x = µ + z
z = (Xµ)
Perform the following unit conversions.
1. GPAs of SUNY Oswego freshman biology majors have approximately
the normal distribution with mean 2.87 and standard deviation .34.
(a) Convert a GPA of 2.00 into standardized units relative to the
mean. (Convert to a Z-score.)
Answer:
(b) If a student’s GPA is 2.5 std above the mean, what is the student’s
GPA?
Answer:
2. The duration of elephant pregnancies from conception to birth varies
according to a distribution that is approximately normal with mean
525 days and standard deviation 32 days.
(a) Convert a duration of 600 days into standardized units relative to
the mean. (Convert to a Z-score.)
Answer:
(b) If the duration of an elephant pregnancy is -1.5 std, then how
many days did the pregnancy last? (Convert from the Z-score
into an X value.)
Answer:
4.11. MODULE 11-12: DISTRIBUTIONS OF RANDOM VARIABLES AND SAMPLE STATISTICS273
3. A forest products company claims that the amount of usable lumber in
its harvested trees averages 172 cubic feet and has a standard deviation
of 12.4 cubic feet. Assume that these amounts have approximately a
normal distribution.
(a) Convert 150 cubic feet into standardized units relative to the
mean. (Convert from X into a Z-score.)
Answer:
(b) Convert a z-score of 1 std above the mean, into cubic feet. Convert
from a Z-score into an X value.
Answer:
4. At two years of age, sardines inhabiting Japanese waters have a length
distribution that is approximately normal with mean 20.20 cm and
standard deviation 0.65 cm. Convert 19.0 cm and 21.0 cm into standardized units relative to the mean.
Answer: 19cm= std.
Answer: 21cm= std.
 PROBABILITY
4.11.2.3 Second Homework on Continuous Random Variables
(Module 11 Topic 2 HW2)
Date Due:
Student’s Name:
Do the following exercises on graph paper and bring it to the classroom
to hand it in. Writeout your verbal responses on the same piece of paper.
1. Graph a continuous unimodal triangular distribution that is symmetric
about the vertical line x=0. Label the coordinates of the x and y
intercepts with numbers so that the total area beneath the distribution
curve will be correct.
2. Sketch a continuous unimodal distribution with a mode at x=0 and
skewed to the right.
3. Sketch a continuous bimodal distribution that is symmetric about the
vertical line x=0.
4. Sketch a continuous trimodal distribution that is symmetric about the
vertical line x=0.
5. Suppose a continuous random variable X has a distribution that is
symmetric about the vertical line x=0. Suppose P(X < 2) = 0.85. (In
other words, suppose that 85% of the population has an X value below
2.) Find P(X < 2). Explain your reasoning and draw a picture to
illustrate your ideas.

SPSS: Multivariate Analysis of Covariance (MANCOVA) -Result
Basically, I’ve conducted a 2×3 (I think) factorial between groups MANCOVA to compare the effects of three different Social Networking Sites (Instagram, Facebook and Twitter) as well as Gender (Male and Female) on subsequent Social comparison scores and Self-esteem scores.
Whilst, accounting for the time spent on the participant’s respective site and their age (covariates). Since these could effect the results.
I’d like you to interpret the data and figure out whether things are significant or not, such as the relationship between each of the three sites and corresponding social comparison and self-esteem scores for men and women or both together. Talk about covariates (Age of the participant and their time spent on their respective site) and if they would of had any impact on their social comparison and self-esteem scores, had we not made them covariates.
The higher the self-esteem score the higher their self-esteem (0-30). The higher the social comparison score the higher the person perceives themselves in comparison to others.
I will attach the SPSS results Output (the word document) but let me know if you would need the raw SPSS data for some reason. I tried to
attach it here but it said wrong file type, but I don’t think you should need it.
My hypotheses were:
1. Facebook users will have the lowest self-esteem scores than Instagram and Twitter users regardless of gender
2. There will be no significant difference between the SC and SE scores of men and women across all platforms
3. The more time spent on any given social networking sitethe lower the user self-esteem will be
If you have any questions feel free to message me

NOTE: Show your work in the problems.

1. In the following situations, indicate whether you’d use the normal distribution, the tdistribution, or neither.
2. The population is normally distributed, and you know the population standard deviation.
   b. You don’t know the population standard deviation, and the sample size is 35.
   c. The sample size is 22, and the population is normally distributed.
   d. The sample size is 12, and the population is notnormally distributed.
   e. The sample size is 45, and you know the population standard deviation.
3. The prices of used books at a large college bookstore are normally distributed. If a sample of 23 used books from this store has a mean price of $27.50 with a standard deviation of $6.75, use Table 10.1 in your textbook to calculate the following for a 95% confidence level about the population mean. Be sure to show your work.
4. Degrees of freedom
   b. The critical value oft
   c. The margin of error
   d. The confidence interval for a 95% confidence level
5. Statistics students at a state college compiled the following two-way table from a sample of randomly selected students at their college:

Answer the following questions about the table. Be sure to show any calculations.

1. How many students in total were surveyed?
   b. How many of the students surveyed play chess?
   c. What question about the population of students at the state college would this table attempt to answer?
   d. State Hºand Hª for the test related to this table.
2. Answer the following questions about an ANOVA analysis involving three samples.
3. In this ANOVA analysis, what are we trying to determine about the three populations they’re taken from?
   b. State the null and alternate hypotheses for a three-sample ANOVA analysis.
   c. What sample statistics must be known to conduct an ANOVA analysis?
   d. In an ANOVA test, what does an Ftest statistic lower than its critical value tell us about the three populations we’re examining?

Table 10.1 Critical t Values