Question

Exercise 1:
On average, six people an hour use a bank's ATM during busy hours at a department store. How likely is it that:
a) exactly six people using the services during a randomly selected hour?
b) less than five people using the services during a randomly selected hour?
c) no one uses the ATM during a 10 minute break?
  d) no one uses the ATM during a 5 minute break?

Exercise 2:
A student has a collection of different grades from different tests which has a normal distribution, an average grade of 100, and a standard deviation of 10. Determine the probability that the student will score:
a) greater than 120;
b) greater than 80;
c) between 85 and 115;
d) greater than 100.

Answer 1

solution: x= 6/ hour -1 xn Poisson P(x) = th x! a) P(x=6) = 6 -6. 6 e (6) 6! 0.1606 4 6 x b) P(x5)= įē loj 0.2851 X=0 X) C = 6 1/10-minute X 10 60 P(x=0) 0.3679 = Oon B 0.3679 x = 6 60 0.5 15-minute d) P(x=0) -0.5 = e 0.6065 10.5) 0) 2) e=100 Oslo Za x-M -4 P(x) 120) - P123 120-100 P/2>2) 0.0228 b) Plx> 80) P(z) 80-100) P/23-2) 0.9772 9 P185 cx (115) 85-100 czi lo 115-100) - 0.8664 = P(-1.5c22 1.5) d) Plx>100) = P1200) 11 0.5000