Final answer:
The student's question involves calculating the probability of certain z-scores under a standard normal distribution using Excel. One can find the proportion of the distribution that lies below a given z-score using the NORM.S.DIST function in Excel and obtain areas to the right by subtracting the left-tail probability from 1.
Step-by-step explanation:
The question pertains to finding probabilities associated with specific z-scores in a standard normal distribution using Microsoft Excel. To calculate these probabilities, one uses Excel functions that correspond to the areas under the normal curve.
A) To find P(z < 0), the proportion of the standard normal distribution below the z-score of 0: In Excel, you would use the formula =NORM.S.DIST(0, TRUE), which will return 0.5, indicating that 50% of the distribution is below the mean of 0.
B) To find P(z < -0.24), use the Excel formula =NORM.S.DIST(-0.24, TRUE). This will return the proportion of the standard normal distribution that lies to the left of the z-score -0.24.
C) To find P(z < -1.13), apply the Excel formula =NORM.S.DIST(-1.13, TRUE) to get the left-tail area under the curve.
D) To find P(Z > -1.81), first find the left-tail probability with =NORM.S.DIST(-1.81, TRUE) and then subtract this value from 1 to get the area to the right of the z-score.