Asked Feb 26, 2019

Part a, b, and c

Find the following probabilities for the standard normal random variable z
a) P(z > 1.46)
b) P(z <-1.56)
c) P(.67 s z<2.41)
d) P(-1.96 sz< -.33)
e) P(z 2 0)
f P(-2.33 z<1.50)

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Find the following probabilities for the standard normal random variable z a) P(z > 1.46) b) P(z <-1.56) c) P(.67 s z<2.41) d) P(-1.96 sz< -.33) e) P(z 2 0) f P(-2.33 z<1.50) 2.


Expert Answer

Step 1

Normal distribution:

A continuous random variable X is said to follow normal distribution with mean (m) and standard deviation (σ) if the probability density function of X is,

Step 2

Standard normal distribution:

The standard normal distribution is a special case of normal distribution. The standard normal distribution will have mean 0 and standard deviation 1. If a random variable X follows normal distribution with mean (m) and standard deviation (σ), then the standard normal variable z will be as given below:

Step 3

An important property of the normal distribution:

The normal distribution is symmetric. Thus, for any pai...


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