The lifespan of a certain brand of bicycle tyre is normally distributed witha mean of 1200km and a std deviation of 80km.
1)Find the probability that a randomly chosen tyre has a lifespan of less than 1100km.
2)Determine the value of A, the nearest integer , if it is found that 4% of the tyres are not road-worthy after A km
For 1), we just use P(X<1100) whr ans is 0.1056, is it?
For 2), how do we do it?
For the first part you find out P(X<1100) by converting it into standard distribution form and then looking up the value of integration from -inf to obtained value from cumulative normal distribution table. For second case you are given the probability as .04. Look up from the table the value of standardised lifespan A and then scale it to given mean and SD. So the second part is just inverse path of first part.