Assessing Manufacturing Tolerances with Normal Distribution
A factory produces ball bearings with diameters that are normally distributed with a mean of 50 mm and a standard deviation of 0.5 mm. Without using a calculator, estimate the probability that a randomly selected ball bearing will have a diameter between 49.5 mm and 50.5 mm.
Part b
Explain in detail how you would compare the experimental frequencies obtained from your data with the expected frequencies derived from a binomial distribution. Specify the statistical test you would use to formally assess the goodness of fit and describe any visual methods for comparison.
Determining the Binomial Success Probability
A manufacturer inspects batches of items and the number of defective items follows a binomial distribution with a fixed number of trials n and an unknown probability of defect p. Given that the expected number of defective items is \(E(X)\) and the variance is \(Var(X)\), answer the following: (a) Express the probability of defect p […]
Empirical Rule Probability Estimation
A data set is normally distributed with a mean of \(\mu\) and a standard deviation of \(\sigma\). Using the Empirical rule, estimate the probability that a randomly selected value lies within one standard deviation of the mean (i.e. between \(\mu – \sigma\) and \(\mu + \sigma\)).
Normal Approximation to a Binomial Distribution
In a smartphone manufacturing process, 8% of the smartphones are found to be defective. If a random sample of 150 smartphones is selected, use the normal approximation with continuity correction to estimate the probability that at most 15 smartphones are defective.