1. Suppose x is a normally distributed random variable withthe random variable, call it x0, such thata) P(x x0)8413b) P(x > x0) = 025c) P(x > x0) = .95d) P(41 Sx < x0) 8630e) 10% of the values of x are less than x0.f) 1% of the values of x are greater than x50 and ơ-3. Find the value of0

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a.b.c

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Step 1

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 y follows normal distribution with mean (m) and standard deviation (s), then the standard normal variable z will be as given below:

Step 2

a.

Find the value of x0 for which P(x x0) = 0.8413:

The random variable x follows normal distribution with mean 50 and standard deviation 3.

That is, m = 50 and s = 3.

The value of x0 for which P(x x0) = 0.8413 is obtained as 53 from the calculation given below:

Step 3

b.

Find the value of x0 for which P(x > x0) = 0.025:

The value of x0 for which P(x > x0) = 0.025 is obtained as 58.88 from the calculation g...

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