Let X be normally distributed with mean -22 and standard deviation ?-16. Use Tab

Question

Let X be normally distributed with mean -22 and standard deviation ?-16. Use Table 1. a. Find PIX s 2). (Round "z" value to 2 decimal places and final answer to 4 decimal places.) X s 2) b. Find PIX > 6). (Round "z value to 2 decimal places and final answer to 4 decimal places.) x> 6) c. Find P/2 s Xs 26). (Round "z" value to 2 decimal places and final answer to 4 decimal places.) 10 sX s 30) (Round "" value to 2 decimal places and final answer to 4 decimal places.) d. Find P(10 s X s 30) (Round "z" value to 2 decimal places and final answer to 4 decimal places.) P(10 s Xs 30)

Explanation / Answer

(1)

Summarizing the data given as follows:

Mean, m = 22

Standard Deviation S' = 16

(a)

At X = 2, we have:

z = (X-m)/S' = (2-22)/16 = -1.25

Using the cumulative z-table, we see:

P(X <= 2) = P(z <= -1.25) = 0.1056

(b)

At X = 6, we have:

z = (X-m)/S' = (6-22)/16 = -1

Using the cumulative z-table, we see:

P(X > 6) = P(z > -1) = 0.8413

(c)

At X = 26, we have:

z = (X-m)/S' = (26-22)/16 = 0.25

Using the cumulative z-table, we see:

P(X <= 26) = P(z < 0.25) = 0.5987

So,

P(2 <= X<= 26) = P(X <= 26) - P(X <= 2) = 0.5987-0.1056 = 0.4931

(d)

At X = 10, we have:

z = (X-m)/S' = (10-22)/16 = -0.75

Using the cumulative z-table, we see:

P(X <= 10) = P(z < -0.25) = 0.2266

At X = 30, we have:

z = (X-m)/S' = (30-22)/16 = 0.5

Using the cumulative z-table, we see:

P(X <= 30) = P(z < 0.5) = 0.6915

So,

P(10 <= X<= 30) = P(X <= 30) - P(X <= 10) = 0.6915-0.2266 = 0.4649

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