Select the answer closest to the specified areas for a N0 1

Select the answer closest to the specified areas for a N(0, 1) density. a) the area to the left of z=-1.52 b) the area to the right z=-0.47

Solution

The distribution N(0,1) corresponds to the standard normal distribution i.e. Z distribution. The area under a probability density function represents the probability of the specified region.

a)

The area to the left of z = -1.52 means -

P(Z < -1.52)

From the Z-table, we get this value as -

P(Z < -1.52) = 0.0643

Hence, area to the left of Z = -1.52 = 0.0643.

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b)

The area to the right of Z = -0.47 means -

P(Z > -0.47)

This can also be written as - P(Z > -0.47) = 1 - P(Z < -0.47)

From the table, we get the value of P(Z < -0.47) = 0.3192

So, P(Z > -0.47) = 1 - 0.3192 = 0.6808

So, the area to the right of Z = -0.47 = 0.6808.