A server receives 160 requests of a certain type every hour. The time to complet

Question

A server receives 160 requests of a certain type every hour. The time to complete a request of this type follows a normal distribution with a mean of5.7 seconds and a standard deviation of0.922 seconds. a) Determine the probability distribution for the time to complete 160 requests. Include the parameters. What is the probability it will take less than 15 minutes to complete all 160 such requests? It is determined the Gamma distribution is a better probability model of the time to complete one request of this type. Now what is the probability that it will take less than 15 minutes to complete all 160 such requests? (An approximate probability is fine.) b) c)

Explanation / Answer

a)

Y = 160 X

X ~N(5.7 , 0.922^2)

Y ~N( 160 * 5.7 , 160 * 0.922^2)

= N( 912,136.01344)

b)

P(Y < 15 *60 )

P(Y < 900)

= P(Z <( 900 - 912)/sqrt(136.01344))

= P(Z < -1.02894)

= 0.1518

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.