Question 6, values are a=4.08, s=0.026, a1=4.078, a2=4.084, b1=4.082, b2=4.087

4. Concrete blocks are tested and it is for that. on average, p% fail to meet the required specification. For a batch of N blocks, determine the probabilities that (a) three blocks and (b) less than four blocks will fail to meet the specification. 5. An automatic machine produces, on average, p% of its components outside of the tolerance required. In a sample of 9 components from this machine, determine the probability of having A components outside of the tolerance required by assuming a binomial dis- tribution. Draw a histogram showing the probabilities of 0. 1, 2.... , 9 components are outside the tolerance required. 6. The mean diameter of holes produced by a drilling machine bit is a mm and the standard deviation of the diameters is s mm. For 20 holes drilled using this machine, determine. correct to the nearest whole number, how many are likely to have diameters of between (a) a1 and oz mm, and (b) by and b2 mm, assuming the diameters ar normally distributed 7. The average useful life of a random sample of 35 similar calculator batteries made on a production line is found to be 98.5 hours contin The sample unarce is 17.89