I\'m not sure how to do problem 1 pictured here. Thank you. Page of 3 -| ZOOM St

Question

I'm not sure how to do problem 1 pictured here. Thank you.

Page of 3 -| ZOOM Staple if there is more than one answer sheet. 1. Let F be an RV that represents the operating temperature in Fahrenheit of one instance of a m process, and let FN(100, 52). Let C be an RV that represents the same process, but measured in Celsius. Fahrenheit can be converted to Celsius using C = F-32). Using Normal table in Canvas, solve for the following (You can also check your answers using R): (a) Find the probability that one randomly selected instance of the process will have operating temperature greater than 98.6 Fahrenheit. (b) Find the distribution of C. (Hint: C~(?,?) (c) Find the probability that one randomly selected instance of the process will have operating temperature below 32 Celsius. 2. Consider a large population which has true mean , and true variance 2, we take a sample of size n 3

Explanation / Answer

F - N(100 ,5^2)

Z = ( F - 100)/5

a)

P(F > 98.6)

= P(Z>(98.6 - 100)/5)

= P(Z > -0.28 )                      {using normal table or excel or R etc}

= 0.6103

b)

C = 5/9 (F -32)

C ~ N( 5/9 * (100 - 32) , (5/9 * 5)^2)

~N( 37.7777, 2.7777^2)

c)

P(C < 32)

= P(Z < ( 32 - 37.7777) / 2.77777)

= P(Z< -2.07997)

= 0.0188

Please rate

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

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