Math Help - question regarding binomial and exponential distributions

Hi

i need help with the attached question

I have attempted the question but i am stuck on parts d) to h)

My answers so far are

a) i substituted in hence my answer was 0.112

b) =0.207

c) =0.117

my guess to part d was
=0.4903

Probability of first three not failing is =0.7 hence answer is =0.7

any help is appreichated

thanks

Hello,

I haven't looked at the other questions yet, but the first one is false

a) i substituted in z=3 hence my answer was 0.112

You're working with a probability density function. The probability of getting a value equal to 3, while working with a rv with pdf, is 0.
What you're asked is the probability that the man fails to do it in 3 minutes. Which means it's the probability that it takes more than 3 minutes to do the task.

So you're looking for P(Z>3), which is , and not

I guess you made the same mistake for question b)

is the answers for part a) =0.223
part b) =0.473

part c) =0.272