he mean number of hours a team of doctors take on an individual operation is 3.1 hours. Assuming the standard deviation is 0.5 hours.

Question

The mean number of hours a team of doctors take on an individual operation is 3.1 hours.
Assuming the standard deviation is 0.5 hours. Find probability that any team of doctors
will spend less than 3.5 hours on an individual’s operation. Assume operation time is
normally distributed random variable.

Answer 1

Hello,

When computing probabilities it's usually easiest to work with z-scores. Any z-score can be computed using the following formula: z = (X - M)/SD, where X is a score, M is the mean and SD is the standard deviation.

For your example, we first want to find the z score that corresponds with 3.5. Using the formula, we find that z = (3.5 - 3.1)/0.5. So z = 0.8.

Noe we want to find what percentage of the normal distribution is below a z-score of 0.8. To do this, you will need a normal distribution table (your teacher should have given you one or there should be one in your textbook). Using the table we see that 78.81% of scores are below 0.8.

Hope that helps.

Answer 2

0.7881446663 using TI-83 DISTR command

binomcdf(-10^9,3.5,3.1,0.5)

 

I just revised the number above...it appears that I miscopied it from my calculator's screen; the calculator command given IS CORRECT.