Mathematics - Statistics Lab Assignment

Week_5NormalDistribution_Math225N_2025.xlsx

Empirical Rule

Enter the data in the blue highlighted area and the results will show in the yellow highlighted area.
				ANSWER
			Empirical Rule	68-95-99.7
	mean	598.4		Lower number	Upper number
	standard deviation	86.7	68%	511.7	685.1
			95%	425	771.8
			99.70%	338.3	858.5

Enter input in blue cells; See answers in yellow cells
Example: Given the first divorce distribution is normally distributed with an average of 28 years and a standard deviation of 5 years we can find the probability that their age is at most 32 (x)using Excel. Answer: 0.7881
				ANSWER
Z score	x	85	Z score	2.5714285714
	mean	58
	standard deviation	10.5
LESS THAN(At most)	AREA LESS THAN	ENTER	Z score	0.8
	Asked to find x	32	Probability Less than F7	0.7881
	Mean	28
	Stdev	5
MORE THAN (at least)	AREA MORE THAN	ENTER	Z score	-0.6666666667
	Asked to find x	12	Probability more than F13	0.7475
	Mean	14
	Stdev	3
	Probability INBETWEEN	ENTER		ANSWER
INBETWEEN	Asked to find Large value	55.4	Probability between F19 and F20 is	0.0927
	Asked to find smaller value	55.2
	Mean	55
	Stdev	0.8006

Enter input in blue cells; See answers in yellow cells
Example: Assume laptop prices are normally distributed with a average of $965 and a standard deviation of $100. The least expensive 5% of laptops cost less than what amount. Answer: $800.52
	Find x given Area/Probability to Right or Left	Enter
	Area to the left	yes	If area to the left is given enter yes; otherwise say no
	Area given	0.05	enter decimal	SUMMARY
	Enter Mean	175		z	-1.644853627
	Enter Standard deviation	11		Find x	156.9066101035
	Find X given Area/Probablity in the middle	Enter
	Area	0.5	enter decimal	SUMMARY
	Enter Mean	81		Lower x	78.3020409992
	Enter Standard deviation	4		Upper x	83.6979590008

Enter the data in the blue highlighted area and the results will show in the yellow highlighted area.
Example: Assume that the game playthrough times for a newly released puzzle game has a mean of 49.8 min and a standard deviation of 4.2 minutes. Given a sample size of n= 39 what is the probability that the sample mean is between 50 and 51 minutes
Answer: 0.34
				CENTRAL LIMIT THEOREM OF MEANS (CLT)
	Step 1:
					ANSWER
	Given	Enter
	n	90		Standard deviation of sample means is SD/sqrt(n)	0.5270
	Standard deviation(SD)	5
	Step 2:
To Calculate Probability	LESS THAN(At most)		MORE THAN (at least)			INBETWEEN
	AREA LESS THAN	ENTER		AREA MORE THAN	ENTER	Probability INBETWEEN	ENTER
	x given	50		x given	51	x Larger value	51
	Mean	49.8		Mean	49.8	x Smaller value	50
	Standard deviation	4.2		Standard deviation	4.2	Mean	49.8
	Sample Size(n)	39		Sample Size(n)	39	Standard deviation	4.2
						Sample size	39
	standard deviation of sample means	0.6725		standard deviation of sample means	0.6725	standard deviation of sample means	0.6725
	Z score	0.2974		Z score	1.7843	Z score for Larger	1.7843
	Probability Less than C23	0.6169		Probability more than G23	0.0372	Zscore for Smaller	0.2974
						Probability between I 18 and I 19 is	0.3446

Enter the data in the blue highlighted area and the results will show in the yellow highlighted area.
Example: According to a study 40% of people have more than $10,000 in credit card debt. Calculate the probability of 60 customers in a company between 21 and 23 have more than $10,000 credit card debt
Answer by using in between probability:
				CENTRAL LIMIT THEOREM OF Proportion( CLT)
	Step 1:
					ANSWER
	Given	Enter
p	Population proportion (Enter decimal = Count /n)	0.4		Standard deviation of sample proportion	0.0632
n	Sample size n	60
	IF COUNT IS GIVEN DIVIDE THIS BY SAMPLE SIZE n to get the PROPORTION
	Step 2:					INBETWEEN
Calculate Probability	LESS THAN(At most)			MORE THAN (at least)
						INBETWEEN	Enter
	LESS THAN	ENTER		MORE THAN	ENTER	Asked Large value Sample proportion	0.38333
	Sample proportion(If count is given then divide this by n)	0.3500	*If count is given = count / n	Sample proportion(count/ n)	0.3833	Asked Small value Sample proportion	0.35000
p	Population proportion	0.4000		Population proportion	0.4000	Population proportion	0.4
	Sample Size (n)	60.0000		Sample Size (n)	60.0000	Sample Size (n)	60.00000
	standard deviation of sample proportion	0.0632		standard deviation of sample proportion	0.0632	standard deviation of sample proportion	0.0632
	Z score	-0.7906		Z score	-0.2635	Z-score of Larger	-0.2635
	Probability Less than F7	0.2148		Probability more than	0.6026	Z-score of smaller	-0.7906
						Probability between I 18 and I 19 is	0.1827