Download 5.4.3 Normal Distribution worksheet

Math 11F
Normal Distribution
Name:
1) The time required for a student to register at university is normally distributed with a mean of 33
minutes and a standard deviation of 6 minutes.
Sketch the normal curve to show the distribution of the registration times.
Mark the points that are 1, 2 and 3 standard deviations from the mean.
What percent of the registrations last:
i)
more than 45 minutes
%
ii)
between 27 minutes and 51 minutes
%
iii)
between 21 and 39 minutes
%
iv)
less than 27 minutes
%
2) An IQ test was given to all members of the armed forces. The results were normally distributed with a
mean of 110 and a standard deviation of 15.
Sketch the normal curve to show the distribution of the test scores.
Mark the points that are 1, 2 and 3 standard deviations from the mean.
According to the test, what is the probability a person scores:
i)
between 110 and 125
ii)
greater than 125
iii)
between 80 and 140
iv)
less than 80
If 75 000 people took the test, how many scored higher than 140?
3) The speeds of vehicles on a city street were recorded for a month period. The results were normally
distributed with a mean of 54 km/h and a standard deviation of 4 km/h.
Sketch the normal curve to show the distribution speeds.
Mark the points that are 1, 2 and 3 standard deviations from the mean.
What percent of vehicles had speeds less than 50 km/h?
%
If the speed limit is 50 km/h, what percent of vehicles are speeding?
%
If 12 000 vehicles use the road each day, how many were going faster than 62 km/h?
4) A manufacturer of AAA batteries needs to determine the distribution of the life of these batteries.
After 120 of these batteries were tested, the average life was found to be 48 hours with a standard
deviation of 5 hours.
Sketch the normal curve to show the distribution of the life of the batteries.
Mark the points that are 1, 2 and 3 standard deviations from the mean.
According to the test, what is the probability of a battery lasting:
i)
between 48 and 58 hours
ii)
greater than 53 hours
iii)
between 43 and 53 hours
iv)
less than 38 hours
If 168 000 batteries were produced, how many would be expected to last between 38 and 53 hrs?