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# If X ~ N(2, 9), computea. P(X ? 2)________________b. P(l ? ISBN: 9780073401331 38

## Solution for problem 4E Chapter 4.5

Statistics for Engineers and Scientists | 4th Edition

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Problem 4E

If X ~ N(2, 9), compute

a. P(X ≥ 2)

b. P(l ≤ X ≤ 7)

c. P(‒2.5 ≤ X ≤ ‒1)

d. P(‒3 ≤ X ‒ 2 ≤ 3)

Step-by-Step Solution:

Step 1 of 4:

Here .

Here mean and

Variance Then, standard deviation  Therefore  standard deviation .

Our goal is:

a). We need to find .

b). We need to find .

c). We need to find .

d). We need to find .

a).

Now we have to compute the .

The formula of the z is

z= We know that mean 2 and standard deviation 3.

Then,    = 1- Using area under the normal curve table. =0.5000. = 1- 0.5000 = 0.5000

Therefore is 0.5000.

Step 2 of 4:

b).

Now we have to find . The formula of the z is

z= We know that 2 and 3. =  =  = and =  =  =   Using area under the normal curve table.  Therefore is 0.5808.

Step 3 of 4

Step 4 of 4

##### ISBN: 9780073401331

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