Let z be a normal random variable with mean 0 and standard deviation 1. What is P(z > -1.1)?Select one:a.0.36432.b.0.8643.c.0.1357.d.-0.1357.e.-0.8643.
Question
Let z be a normal random variable with mean 0 and standard deviation 1. What is P(z > -1.1)?
Select one:
a. 0.36432.
b. 0.8643.
c. 0.1357.
d. -0.1357.
e. -0.8643.
Solution
To solve this problem, we need to understand the properties of a standard normal distribution. A standard normal distribution has a mean of 0 and a standard deviation of 1. The total area under the curve of this distribution is 1, representing the total probability.
The question asks for the probability that z is greater than -1.1. In terms of the standard normal distribution, this is equivalent to finding the area under the curve to the right of z = -1.1.
We can find this value using a standard normal distribution table or a calculator with a normal distribution function. The value for P(Z > -1.1) is equivalent to 1 - P(Z < -1.1).
Looking up -1.1 in the Z-table, we find that P(Z < -1.1) = 0.1357.
Therefore, P(Z > -1.1) = 1 - P(Z < -1.1) = 1 - 0.1357 = 0.8643.
So, the correct answer is b. 0.8643.
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