Question

) A bicycle company claims their bikes will go for a mean µ = 20,000 miles before service is required,
      with a standard deviation of s = 340 miles, normally distributed. You take a sample of 46 bikes

      a) what is the probability your sample mean is 19,950 or less?

      b) what is the probability that your sample mean is between 19,900 and 20,080?

Answer 1

1.

Suppose, random variables denote miles before requirement of a service for i-th (i=1,2,...,46) bicycle.

(a)

Required probability is given by

= 0.1592848    [Using R-code 'pnorm(-0.9974016)']

(b)

Required probability is given by

= 0.9217059    [Using R-code 'pnorm(1.595843)-pnorm(-1.994803)']