Statistics and R problem Please answer these questions with step and code (if yo

Question

Statistics and R problem Please answer these questions with step and code (if you can ) as much as possible, thanks!

The lifetime of each of the flashlight batteries I just purchased is distributed
as a Gamma random variable with mean of 100 hours and
standard deviation 10 hours. My flashlight needs just one battery to
operate, and when one battery dies, I immediately replace it with a
new battery. What is the probability that my batteries will power the
flashlight for at most 200 hours? What is the probability that my batteries
will power the flashlight for at least 900 hours?

Explanation / Answer

we can approximate gamma distribution with standardized normal distribution z=(x-mean)/(sd)

mean=100

sd=10

for x=200 , z=(200-100)/10=10

p(x<200)=p(z<10)=0

for x=900, z=(900-100)/10=90

p(x>900)=p(z>90)=0

so both the probability would zero

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