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16. The mean of a normal probability distribution is 400 pounds. The standard deviation is 10...


16. The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds. a. What is the area between 415 pounds and the mean of 400 pounds? . a. .4332 b. .1915 c. .3085 b What is the area between the mean and 395 pounds? .с. What is the probability of selecting a value at random and discovering that it has a value of less than 395 pounds?
16. The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds. a. What is the area between 415 pounds and the mean of 400 pounds? . a. .4332 b. .1915 c. .3085 b" What is the area between the mean and 395 pounds? .с. What is the probability of selecting a value at random and discovering that it has a value of less than 395 pounds?
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Answer #1

16)

Solution :

Given that ,

mean = \mu = 400

standard deviation = \sigma = 10

(a)

P(400 < x < 415) = P((400 - 400 / 10) < (x - \mu ) / \sigma < (415 - 400) / 10) )

= P(0 < z < 1.5)

= P(z < 1.5) - P(z < 0)

= 0.9332 - 0.5 = 0.4332

Probability = 0.4332

(b)

P(395 < x < 400) = P((395 - 400 / 10) < (x - \mu ) / \sigma < (400 - 400) / 10) )

= P(-0.5 < z < 0)

= P(z < 0) - P(z < -0.5)

= 0.5 - 0.3085 = 0.1915

Probability = 0.1915

(c)

P(x < 395) = P((x - \mu ) / \sigma < (395 - 400) / 10) = P(z < -0.5)

Using standard normal table,

P(x < 395) = 0.3085

Probability = 0.3085

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