Suppose x is a normally distributed random variable with u = 13 and o = 2. Find each of the following probabilities. a. P(x2 14) b. P(xS9.5) c. P(13.5 sxs17.6) d. P(8.22 sxs15.76) Click here to view a table of areas under the standardized normal curve. 1. P(x2 14)= .309 (Round to three decimal places as needed.) . P(xs9.5)= .04 (Round to three decimal places as needed.) =. P(13.5sxs 17.6) = .391 (Round to three decimal places as needed.) 1. P(8.22 sxs 15.76) = (Round to three decimal places as needed.)

MATLAB: An Introduction with Applications
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Suppose \( x \) is a normally distributed random variable with \( \mu = 13 \) and \( \sigma = 2 \). Find each of the following probabilities:

a. \( P(x \geq 14) \)  
b. \( P(x \leq 9.5) \)  
c. \( P(13.5 \leq x \leq 17.6) \)  
d. \( P(8.22 \leq x \leq 15.76) \)  

Click here to view a table of areas under the standardized normal curve.

**Solutions:**

a. \( P(x \geq 14) = 0.309 \) (Round to three decimal places as needed.)

b. \( P(x \leq 9.5) = 0.04 \) (Round to three decimal places as needed.)

c. \( P(13.5 \leq x \leq 17.6) = 0.391 \) (Round to three decimal places as needed.)

d. \( P(8.22 \leq x \leq 15.76) = \) (Round to three decimal places as needed.)

Please refer to the standard normal distribution table to find these areas accurately. The values provided have been rounded to three decimal places for precision.
Transcribed Image Text:Suppose \( x \) is a normally distributed random variable with \( \mu = 13 \) and \( \sigma = 2 \). Find each of the following probabilities: a. \( P(x \geq 14) \) b. \( P(x \leq 9.5) \) c. \( P(13.5 \leq x \leq 17.6) \) d. \( P(8.22 \leq x \leq 15.76) \) Click here to view a table of areas under the standardized normal curve. **Solutions:** a. \( P(x \geq 14) = 0.309 \) (Round to three decimal places as needed.) b. \( P(x \leq 9.5) = 0.04 \) (Round to three decimal places as needed.) c. \( P(13.5 \leq x \leq 17.6) = 0.391 \) (Round to three decimal places as needed.) d. \( P(8.22 \leq x \leq 15.76) = \) (Round to three decimal places as needed.) Please refer to the standard normal distribution table to find these areas accurately. The values provided have been rounded to three decimal places for precision.
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