A national dental association conducted a survey to find the average (mean) amount of time dentists spend on dental fillings per
week. Based on a simple random sample, they surveyed 144 dentists. The statistics showed that dentists spent an average of 20 hours per week on fillings with a standard deviation of 10 hours. What is the probability of finding a sample mean less than 18 hours?
The probability of finding a sample mean less than 18 hours is 0.0082
Step-by-step explanation:
To find the probability of finding a sample mean less than 18 hours, we need to calculate the z-score of this sample mean 18. And the probability of finding a sample mean less than 18 hours is P(z<z(18)).
Z-score can be calculated as follows:
z(18)= where
X is the sample mean (18 hours)
M is the average hours dentists spend per week on fillings (20 hours)
s is the standard deviation (10 hours)
N is the sample size (144)
Putting the numbers, we get:
z(18)=
Using z- table we can find that P(z<z(18)) = 0.0082