Let F be an RV that represents the operating temperature in Fahrenheit of one in

Question

Let F be an RV that represents the operating temperature in Fahrenheit of one instance of a manufacturingprocess, and let F N(90, 25). Let C be an RV that represents the same process, but measured in Celsius.Fahrenheit can be converted to Celsius using Celsius = 59 (Fahrenheit32). (I would suggest doing these with a hand calculator and normal table as practice for exam conditions, but you may checkyour answers in R if you wish.)

(a) Find the probability that one randomly selected instance of the process will have operating temperaturegreater than 93.8 Fahrenheit.
(b) Find the distribution of C. The distribution will consist of the ’family’ of distribution (for example,Bernoulli, Binomial, Normal, etc.) plus the relevant parameters associated with that family ( for aBernoulli, n and for a Binomial, µ and 2 for a Normal, etc.).
(c) Find the probability that one randomly selected instance of the process will have operating temperaturebelow 29 Celsius.

Explanation / Answer

here mean =90

and std deviation =(25)1/2=5

a) P(X>93.8)=1-P(X<93.8)=1-P(93.8-90)/5)=1-P(Z<0.76)=1-0.7764=0.2236

b) it is normal distribution with µ =90 and 2 =25

c) here 29 degree celsius =(9/5)*29+32 =84.2 Fahrenheit

P(X<84.2)=P(Z<(84.2-90)/5)=P(Z<-1.16)=0.1230

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