According to an Occupational and Health Safety Administration (OHSA) 2014 report, a hospital is one of the most dangerous places to work. The major cause of injuries that result in missed work was overexertion. Almost half (48%) of the injuries that result in missed work were due to overexertion. Let x be the number of hospital-related injuries caused by overexertion.
a. Explain why x is approximately a binomial random variable.
b. Use the OHSA report to estimate p for the binomial random variable of part a.
c. Consider a random sample of 100 hospital workers who missed work due to an on-the-job injury. Use the p from part b to find the mean and standard deviation of p̂, the proportion of the sampled workers who missed work due to overexertion.
d. Refer to part c. Find the probability that the sample proportion is less than .40.