A random variable follows the normal probability distribution with a mean of 100

Question

A random variable follows the normal probability distribution with a mean of 100 and a standard deviation of 10. Determine the probability for a randomly selected value from this population in parts a through d below. a. What is the probability that the value is less than 80? The probability that the value is less than 80 is 0228 (Round to four decimal places as needed.) b. What is the probability that the value is less than 75? The probability that the value is less than 75 is .0062 (Round to four decimal places as needed.) c.What is the probability that the value is more than 110? The probability that the value is more than 110 is .1587 (Round to four decimal places as needed.) d. What is the probability that the value is more than 85? The probability that the value is more than 85 is .9332 Round to four decimal places as needed.)

Explanation / Answer

Solution :

Given that mean µ = 100 ,standard deviation = 10

a. P(x < 80) = P((x - µ)/ < (80 - 100)/10)

= P(Z < -2)

= 0.0228

b. P(x < 75) = P((x - µ)/ < (75 - 100)/10)

= P(Z < -2.5)

= 0.0062

c. P(x > 110) = P((x - µ)/ > (110 - 100)/10)

= P(Z > 1)

= 0.1587

d. P(x > 85) = P((x - µ)/ > (85 - 100)/10)

= P(Z > -1.5)

= 0.9332

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