answer with full solutions please

(Keep 4 decimal places if necessary) The television picture tubes of manufacturer A have a mean lifetime of 10.5 years and a standard deviation of 3 years, while those of manufacturer B have a mean lifetime of 10.0 years and a standard deviation of 3 years. A random sample of 40 tubes from manufacturer A is selected and another sample of 50 tubes from manufacturer B is selected randomly. a) What is the probability that the sample mean from manufacturer A falls between 10 and 11 years? b) What is the probability that the sample from manufacturer A will have a mean lifetime that is at least 1 year more than the mean lifetime of the sample from manufacturer B? c) Recall that we learned how to calculate the sample size in Chapter 10. The sample size 50 above for manufacturer B is calculated in that way. Now suppose that the bound on the error of estimation is reduced by half and that nothing else is changed, what could the new sample size for manufacturer B become