suppose x is a normally distributed random variable with his Question: 1 pt 6 of

Question

suppose x is a normally distributed random variable with his Question: 1 pt 6 of 7 (5 complete) Suppose x is a normally distributed random variable with-11 and ?-2 Find each of the following probabilities. a. P(x 2 14) b. P(xs 10.5) c. P(11.44sx 16.56) d. P(6.28sxs 1384) Click here to view a table of areas under the standardized normal curve. a. P(x214)-? (Round to three decimal places as needed.) b.P(xs 10.5)-Q (Round to three decimal places as needed ) c. P(11.44 sxs16 56)(Round to three decimal places as needed) d. P(6 28 sxs 13.84)-(Round to three decimal places as needed) ra w to Enter your answer in each of the answer boxes All A TOSHIBA

Explanation / Answer

Mean, u = 11

Standard deviation , s = 2

(a) For X = 14

Z score = ( X - u )/ s = 1.5

From z table, P( X>= 14) = 0.067

(b) For X = 10.5

Z score = (10.5 - 11)/2 = -0.25

From z table, P( X <= 10.5 ) = 0.401

(c) For X = 11.44

Z = 0.22

For X = 16.56

Z = 2.78

From z table , P (1.44 <= X <= 16.56) = 0.4973 - 0.0832 = 0.414

(d) For X = 6.28

Z = -2.36

For X = 13.84

Z = 1.42

From z table, P(6.28 <= X <= 13.84) = 0.4909 + 0.4222 = 0.913

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