Some of my classmates, including myself find it difficult when to use the different formulas in finding the z-value. But our teacher, Ms. Macatigos explained further the idea when to use this different formulas.
Acccording to her, the formula z = value- mean / standard deviation is used to gain information about an individual data value obtained from the population while the formula z = value- population mean / standard deviation/ square root of n is used to gain information about a sample mean.
Consider the problems below for more clarification:
* The average number of pounds of rice a person consumes a year is 225 pounds. Assume that the standard deviation is 30 pounds and the distribution is normally distributed. Find the probability that a person selected at random consumes less than 215 pounds per year.
Solution: z = 215-225/ 30
= -0.34
P(x less than 215) = P(z less than -0.34)
= 0.5- 0.1331
=0.3669
- we use the first formula because the question asks about an individual person.
But if the question will be, " If a sample of 35 individuals is selected, find the probability that the mean of the sample will be less than 215 pounds per year.
Solution: z = 215-225/ 30 / square root of 35
= -10/ 5.71
= -1.75
P(x less than 215 ) = P(z less than -1.75 )
= 0.5 - 0.4599
= 0.0401
- we use the second formula because the question concerns the mean of a sample with a size of 35.
I hope it will become more easier for us to know what formula will we use in finding the z- value after the examples I had given.
By: Dustin Joshua Esquia III- Gold
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