Question

For this submission, you will be given a series of scenarios and small collections of data. You should plot the data or calculate probabilities using excel. Then, you will create your own real or hypothetical scenario to graph and explain.

Answer the following:

The mean temperature for the month of July in Boston, Massachusetts is 73 degrees Fahrenheit. Plot the following data, which represent the observed mean temperature in Boston over the last 20 years:

1998	72
1999	69
2000	78
2001	70
2002	67
2003	74
2004	73
2005	65
2006	77
2007	71
2008	75
2009	68
2010	72
2011	77
2012	65
2013	79
2014	77
2015	78
2016	72
2017	74

Is this a normal distribution? Explain your reasoning.

What is an outlier? Are there any outliers in this distribution? Explain your reasoning fully.

Using the above data, what is the probability that the mean will be over 76 in any given July?

Using the above data, what is the probability that the mean will be over 80 in any given July?

Answer 1

(a)

Mean:72.65

Median: 72.5

Mode: 72.77

Normal Distribution is a symmetric distribution. With this said, the mean, median and the mode are all the same for a normal distribution.

The equality of the mean, median and mode makes a normal distribution curve to be a Bell curve . This is the graphical representation of a normal distribution curve :-

Here in the graph you can see :-

• Mean = Median = Mode.
• Symmetry in the center. This means that the distribution is symmetrically skewed.
• 50% of the data is to the left to the mean and remaining 50% is to the right of the mean.
• And of course, it is a Bell shaped curve.

(b) In statistics, an outlier is an observation point that is distant from other observations. An outlier may be due to variability in the measurement or it may indicate experimental error; the latter are sometimes excluded from the data set.

Outlier detected?	No
Significance level:	0.05 (two-sided)
Critical value of Z:	2.70824545658

Your data

Row	Value	Z	Significant Outlier?
1	72.	0.15
2	69.	0.84
3	78.	1.23
4	70.	0.61
5	67.	1.30
6	74.	0.31
7	73.	0.08
8	65.	1.76	Furthest from the rest, but not a significant outlier (P > 0.05).
9	77.	1.00
10	71.	0.38
11	75.	0.54
12	68.	1.07
13	72.	0.15
14	77.	1.00
15	65.	1.76
16	79.	1.46
17	77.	1.00
18	78.	1.23
19	72.	0.15
20	74.	0.31

(c)

Sample Standard Deviation, s

4.34408

Mean=72.65

Since we are asked about the mean (not an individual observation), we need to calculate the standard deviation for the mean: ?_x = 4.34408 / ? 20 = 0.9714.

Now, we calculate the z-score, z = 76?72.65 / 0.9714 = 3.4486

The P-Value is 0.000282.

(d)

Since we are asked about the mean (not an individual observation), we need to calculate the standard deviation for the mean: ?_x = 4.34408 / ? 20 = 0.9714.

Now, we calculate the z-score, z = 80?72.65 / 0.9714 = 7.566

The P-Value is < 0.00001

This number is larger than the z-scores on the table, so we can assume that the table would give us (approximately) 1. Since we are asked about “greater than,” we need to subtract this probability from 1, so we get 1 ? 1 = 0.