Question

A study was made of seat belt use among children who were involved in car crashes that caused them to be hospitalized. It was found that children not wearing any restraints had hospital stays with a mean of 7.37 days and a standard deviation of 2.75 days with an approximately normal distribution. (a) Find the probability that their hospital stay is from 5 to 6 days, rounded to five decimal places. (b) Find the probability that their hospital stay is greater than 6 days, rounded to five decimal places.

Answer 1

Since number of days stayed following approximately normal distribution we can convert normal variate to standard normal variate and the with the help of standard normal table we calculate the required probabilities or area.

Standard normal curve is symmetric about zero hence P(Z<=-z)=P(Z>=z)

And P(Z>=-z) = 0.5 + P(0<=Z<=z) since area on both side of mean(0) is 0.5 equally divided.