Question

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?

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