Consider a normal population with ì = 49 and ó = 6. Calculate the z-score for an x of 44.2 from a sample of size 22. (Give your answer correct to two decimal places.)
44.2-49/6/22^=.00165=.00
To calculate the z-score for a given x value, we can use the formula:
z = (x - μ) / (σ / √n)
Where:
- x is the observed value
- μ is the mean of the population
- σ is the standard deviation of the population
- n is the sample size
In this case, the given x value is 44.2, the mean μ is 49, the standard deviation σ is 6, and the sample size n is 22.
Now we can plug these values into the formula:
z = (44.2 - 49) / (6 / √22)
Calculating the numerator:
44.2 - 49 = -4.8
Calculating the denominator:
6 / √22 ≈ 1.2767
Now we can calculate the z-score:
z = -4.8 / 1.2767 ≈ -3.76
Rounding to two decimal places, the z-score for an x value of 44.2 from a sample of size 22 is approximately -3.76.