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Section 5.3

Section 5.3. Normal Distributions Finding Probabilities. 100. 115. Probabilities and Normal Distributions. If a random variable, x is normally distributed, the probability that x will fall within an interval is equal to the area under the curve in the interval.

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Section 5.3

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  1. Section 5.3 Normal Distributions Finding Probabilities

  2. 100 115 Probabilities and Normal Distributions If a random variable, x is normally distributed, theprobabilitythat x will fall within an interval is equal to the area under the curve in the interval. IQ scores are normally distributed with a mean of 100 and standard deviation of 15. Find the probability that a person selected at random will have an IQ score less than 115. To find the area in this interval, first find the standard score equivalent to x = 115.

  3. Normal Distribution Find P(x < 115) SAME 100 115 SAME 1 0 Probabilities and Normal Distributions Standard Normal Distribution Find P(z < 1) P( z < 1) = 0.8413, so P( x <115) = 0.8413

  4. Normal Distribution Application Monthly utility bills in a certain city are normally distributed with a mean of $100 and a standard deviation of $12. A utility bill is randomly selected. Find the probability it is between $80 and $115. P(80 < x < 115) P(-1.67 < z < 1.25) 0.8944 - 0.0475 = 0.8469 The probability a utility bill is between $80 and $115 is 0.8469.

  5. Suppose that the height of UCLA female students has normal distribution with mean 62 inches and standard deviation 8 inches. What percentage of all these heights are less than 58 inches long?

  6. A firm's marketing manager believes that total sales for next year will follow the normal distribution, with mean of $2.5 million and a standard deviation of $300, 000. What is the probability that the firm's sales will be more than $220,000?

  7. The lengths of the sardines received by a certain cannery is normally distributed with mean 4.62 inches and a standard deviation 0.23 inch. What percentage of all these sardines is between 4.35 and 4.85 inches long?

  8. The heights of six-year old girls are normally distributed with • a mean of 117.80 cm and a standard deviation of 5.52 cm. • Find the probability that a randomly selected six-year old girl • has a height between 117.80 and 120.56 cm. • A student has computed that it takes an average of 17 minutes • with a standard deviation of 3 minutes to drive from home, park • the car, and walk to an early morning class. What is the • probability that a student took less than21 minutes to get to class? • A company called Camp Comfort makes down-filled sleeping • bags. The amount of down in an adult sleeping bag has a • mean of 32 oz. and a standard deviation of 0.9 oz. What is • the probability that a bag chosen at random has more than • 33.2 oz?

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