# Distribution of Temperatures - Descriptive and General Statistics

Problem 1: Using Symbols

Word-process the symbol for population standard deviation (sigma) in the space below:

Using Subscripts

Word-process the symbol for population standard deviation with subscript x (sigma subscript x) in the space below:

Using Equations

Word-process the following five equations:

k= N/n

z= (x ̅-μ)/(σ/√n)

z=(x ̅-μ)/(σ/√n √((N-n)/(N-1)))

p ̂=x/n

z=(p ̂-p)/√((p∙q)/n)

Using Drawing Tool to Create Diagrams

Suppose in a large department store, the average number of shoppers is 448, with a standard deviation of 21 shoppers. We are interested in the probability that a random sample of 49 different shoppers will yield a sample mean between 441 and 446 shoppers. Create and attach a normal curve to this document with the following elements: the normal curve, a label of the average number of shoppers, and labels for the sample means of 441 and 446 shoppers. Include all the appropriate symbols.

Problem 2: Descriptive Statistics

The monthly average low temperatures* during different months of year at Manchester, NH are given below:

January February March April May June

5 8 18 29 40 50

July August September October November December

55 53 44 32 24 12

Word-process your solutions and answers below. Copy and paste your Excel work under the appropriate question below. Expand the space as necessary.

a) Find the mean yearly low temperature based on the monthly averages by applying the formulas (without using computer software).

b) Find the standard deviation of the monthly low temperatures by applying the formulas (without using computer software).

c) If the above data was a sample, what would be the sample standard deviation? Compute by applying the formulas (without using computer software).

d) Copy and paste the data from this document to Excel. Use functions in Excel to compute the mean, population standard deviation and sample standard deviation. Copy and paste your spreadsheet work into this Word document.

e) Create a histogram using MS Excel. Comment on the distribution of monthly low temperatures. Copy and paste your spreadsheet work into this Word document. Hint: use 9, 19, 29, 39, 49 for the bins.

#### Solution Preview

Please see the attachment for the images.

when x ̅=441,z=(x ̅-µ)/( σ/√n)=(441-448)/(21/√49)=-2.33

when x ̅=446,z=(x ̅-µ)/( σ/√n)=(446-448)/(21/√49)=-0.67

P(-2.33<z<-0.67)=P(z<-0.67)-P(z<-2.33)=0.2514-0.0099=0.2415.

Therefore, the probability that a random sample of 49 different shoppers will yield a sample mean between 441 and 446 shoppers is around 0.2415

Problem 2: Descriptive Statistics

a) Find the mean yearly low temperature based on the monthly averages by applying the formulas (without using computer software).

x ...

#### Solution Summary

The solution discusses the distribution of temperatures including descriptive and general statistics.