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MATH399 Statistics
Week 4 Lab
Name: Math 399N final
Statistical Concepts:
- Probability
- Binomial Probability Distribution
Calculating Binomial Probabilities
➢ Open a new Excel worksheet.
- Open spreadsheet
- In cell A1 type “success” as the label
- Under that in column A, type 0 through 10 (these will be in rows 2 through 12)
- In cell B1, type “one fourth”
- In cell B2, type “=BINOM.DIST(A2,10,0.25,FALSE)” [NOTE: if you have
Excel 2007, then the formula is BINOMDIST without the period]
- Then copy and paste this formula in cells B3 through B
- In cell C1, type “one half”
- In cell C2, type “=BINOM.DIST(A2,10,0.5,FALSE)”
- Copy and paste this formula in cells C3 through C
- In cell D1 type “three fourths”
- In cell D2, type “=BINOM.DIST(A2,10,0.75,FALSE)”
- Copy and paste this formula in cells D3 through D
Plotting the Binomial Probabilities
- Create plots for the three binomial distributions above. You can create the scatter
plots in Excel by selecting the data you want plotted, clicking on INSERT, CHARTS,
SCATTER, then selecting the first chart shown which is dots with no connecting
lines. Do this two more times and for graph 2 set Y equal to ‘one half’ and X to
‘success’, and for graph 3 set Y equal to ‘three fourths’ and X to ‘success’. Paste
those three scatter plots in the grey area below. (12 points)
one fourth
Probability 0.
0 0 2 4 6
Success
8 10 12
one half
Probability
0 (^0 2 4 )
Success
8 10 12
P(x=0) (^) 0.
P(x=1) (^) 0.
P(x=2) (^) 0.
P(x=3) 0.
P(x=4) 0.
P(x=5) (^) 0.
P(x=6) (^) 0.
P(x=7) (^) 0.
P(x=8) (^) 0.
P(x=9) 0.
P(x=10) 0.
P(x≥1) 0.
P(x>1) 0.
P(4<x ≤7) 0.
P(x<0) 0
P(x≤4) 0.
P(x<4 or x≥7) 0.
- List the probability value for each possibility in the binomial experiment calculated at
the beginning of this lab, which was calculated with the probability of a success being
½. (Complete sentence not necessary; round your answers to three decimal places)
(10 points)
- Give the probability for the following based on the calculations in question 3 above,
with the probability of a success being ½. (Complete sentence not necessary; round
your answers to three decimal places) (12 points)
- Calculate (by hand) the mean and standard deviation for the binomial distribution
with the probability of a success being ½ and n = 10. Either show work or explain
how your answer was calculated. Use these formulas to do the hand calculations:
Mean = np , Standard Deviation = (4 points)
Mean = np :
= 10 ×^
Standard Deviation = :
npq
= (^) √ 10 × 0.5 × 0.5=1.
npq
When you flip a coin, there are two possible outcomes: heads and tails. Each outcome has
a fixed probability, the same from trial to trial. In the case of coins, heads and tails each
have the same probability of ½. The distribution of tossing a fair coin is symmetrical just
like binomial distribution.
The four properties of a binomial experiment exists of a fixed number for the trials with
each one having two out comes: successes and failures. The outcomes are to be totally
independent of the other. The numbers are independent, 2 outcomes are documented, the
number of
Mean from question #2: = 4.
Standard deviation from question #2: =1.
Mean from question #5: =
Standard deviation from question #5: =1.
Comparison and explanation:
Mean and standard deviation of question 5 are higher than those in question 2 but with a
very small magnitude. This shows higher probability of successes
- Using all four of the properties of a Binomial experiment (see page 201 in the
textbook) explain in a short paragraph of several complete sentences why the Coin
variable from the class survey represents a binomial distribution from a binomial
experiment. (4 points)
- Compare the mean and standard deviation for the Coin variable (question 2) with
those of the mean and standard deviation for the binomial distribution that was
calculated by hand in question 5. Explain how they are related in a short paragraph of
several complete sentences. (4 points)
