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A normal distribution has mean x and standard deviation σ . For a randomly selected x -value from the distribution, find P( x – 2σ ≤ x ≤ x ). x. x. x. x. The probability that a randomly selected x -value lies between – 2 σ and is the shaded area under the normal curve shown.

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**A normal distribution has mean xand standard deviation σ.**For a randomly selected x-value from the distribution, find P(x – 2σ ≤ x ≤ x). x x x x The probability that a randomly selected x-value lies between –2σ and is the shaded area under the normal curve shown. P(–2σ ≤ x ≤ ) EXAMPLE 1 Find a normal probability SOLUTION = 0.135 + 0.34 = 0.475**Readings higher than 200 are considered undesirable. About**what percent of the readings are undesirable? b. EXAMPLE 2 Interpret normally distribute data Health The blood cholesterol readings for a group of women are normally distributed with a mean of 172 mg/dl and a standard deviation of 14 mg/dl. a. About what percent of the women have readings between 158 and 186?**a. The readings of 158 and 186 represent one standard**deviation on either side of the mean, as shown below. So, 68% of the women have readings between 158 and 186. EXAMPLE 2 Interpret normally distribute data SOLUTION**b. A reading of 200 is two standard deviations to the**right of the mean, as shown. So, the percent of readings that are undesirable is 2.35% + 0.15%, or 2.5%. EXAMPLE 2 Interpret normally distribute data**A normal distribution has mean and standard deviation σ.**Find the indicated probability for a randomly selected x-value from the distribution. x x P(≤ ) x 1. ANSWER 0.5 for Examples 1 and 2 GUIDED PRACTICE**P(> )**x 2. x ANSWER 0.5 for Examples 1 and 2 GUIDED PRACTICE**P(<< + 2σ )**x 3. x x ANSWER 0.475 for Examples 1 and 2 GUIDED PRACTICE**P( – σ<x<)**x x ANSWER 0.34 for Examples 1 and 2 GUIDED PRACTICE 4.**P(x ≤ – 3σ)**5. x ANSWER 0.0015 for Examples 1 and 2 GUIDED PRACTICE**P(x > + σ)**6. x ANSWER 0.16 for Examples 1 and 2 GUIDED PRACTICE**WHAT IF?In Example 2, what percent of the women have**readings between 172 and 200? 7. ANSWER 47.5% for Examples 1 and 2 GUIDED PRACTICE

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