Download Calculating Standard Deviation

Calculating Standard Deviation
Normal Distribution
Normal Distribution
1) The length of similar components produced by a company are approximated by a normal distribution model with
a mean of 5 cm and a standard deviation of 0.02 cm. If a component is chosen at random
a) What is the probability (%) that the length of this component is between 4.98 and 5.02 cm?
b) what is the probability (%) that the length of this component is between 4.96 and 5.04 cm?
2) The annual salaries of employees in a large company are approximately normally distributed with a mean of
$50,000 and a standard deviation of $10,000.
a) What percent of people earn less than $40,000?
b) What percent of people earn between $60,000 and $70,000?
c) What percent of people earn more than $70,000?
3) A radar unit is used to measure speeds of cars on a motorway. The speeds are normally distributed with a
mean of 90 km/hr and a standard deviation of 10 km/hr. What percent of cars would be traveling at more than
100 km/hr?
4) The average life span of a tire is 20,000km with a standard deviation of 1700km. The life span of tires is
normally distributed.
a)
b)
c)
Draw the normal curve for this situation.
How many tires should last between 16,600km and 21,700km if the sample size is 5000 tires.
How many tires should last longer than 21,700km?
5) The lifespan of a premium tire on average is 20,000 km with a standard deviation of 500 km. A random sample
of 5 tires are selected from a new tire line and they lasted the following distances:
20,200 km, 19,000 km, 21,200 km, 20,100 km, and 19,600km
If ANY RANDOM SAMPLE of 5 has a standard deviation greater than 500 km, this means that the new tire
does not meet standards. Does this sample meet standard?
6) The lifespan of a bulb is 10,000 hours with a standard deviation of 400 hours. The lifespan of a bulb is normally
distributed; draw a normal curve for this situation.
a) If 300 bulbs are testes, how many should last between 9,600 hours and 10,880 hours?
7) 99.7% of people own a car between 2 years and 8 years. The amount of time a person owns a car is normally
distributed. Draw a normal curve to represent this information. 410 people own a car between 4 and 7 years,
what is the size of the original sample?
8) 68% of male humans grow between 66 inches and 78 inches tall. The growth of male humans is normally
distributed.
d)
e)
f)
Draw the normal curve for this situation.
900 males represent 68% of a sample taken. What is the original sample size?
How many males from this sample would we expect to be less than 66 inches tall?