Given that z is a standard normal random variable, compute the following probabilities (to 4 decimals).
c. P(z -1.5)
d. P(z -2.5)
This is what I got too but the web where I do my homework says it is wrong.
To compute the probability for a standard normal random variable, you need to use a standard normal distribution table or a calculator. Here's how you can find the probabilities for the given values:
c. P(z < -1.5):
To find this probability, you need to find the area under the standard normal curve to the left of -1.5. You can use a standard normal distribution table or a calculator to get the exact value.
If using a standard normal distribution table, you need to find the row corresponding to -1.5 and the column corresponding to the decimal portion. The intersection of this row and column will give you the value, which represents the probability.
If using a calculator, you can use the cumulative distribution function (CDF) of the standard normal distribution. Enter -1.5 as the input and the calculator will return the probability.
d. P(z < -2.5):
Similarly, to find this probability, you need to find the area under the standard normal curve to the left of -2.5. Again, you can use either a standard normal distribution table or a calculator to find the value.
Using these methods, you can obtain the probabilities with 4 decimal places for the given values of z.
c. P(z < -1.5) = 0.0062
d. P(z< -2.5) = 0.0668
C. P(Z>-1.5) =0.9938
d. P (Z>-2.5) =0.9332