The Empirical Rule
The % of data within 1 standard deviation of the mean.
68%
The command in your calculator used to find the area under a curve.
Normalcdf
The area to the right of the mean in a perfectly symmetric curve.
0.5
The area between z=-1 and z=1
0.68
The z-score that marks the 50th percentile.
z=0
The % of data that falls between z=-2 and z=2
95%
Find the area to the left of z=-1.5 (Round 2 decimal places)
0.07
Find the area to the right of z = 1.25 (Round 2 decimal places)
0.11
Find the area between x=45 and x=55 if mean=50 and SD=5
0.68
Find the z-score for the 90th percentile.
z=1.28
With a mean of 100 and standard deviation of 10, what two values is 99.7% of data between?
70, 130
What is the calculator input for P(z<-0.15)
Normalcdf(-100, -0.15, 0, 1)
What is the calculator input for P(z>1.42)
Normalcdf(1.42, 100, 0, 1)
The calculator input for the area between z=1.1 and z=2.3
Normalcdf(1.1, 2.3, 0, 1)
A factory produces metal rods that must be a specific length to fit into an engine. The lengths of these rods are normally distributed with a mean of 25.0 cm and a standard deviation of 0.08 cm.
The quality control team will only accept the middle 90% of the rods produced. What are the minimum and maximum lengths a rod can be to be accepted?
24.87cm and 25.13cm
The % of data that falls specifically between z=1 and z=2
13.5%
Calculate the area for P(z<2.12) (Round 2 decimal places)
0.98
Calculate the area for P(z>-0.85)
0.80
Find the area between z=-1.02 and z=2.32
0.84
A frozen food company wants to identify the lightest 10% of their "1-lb packages" to check for machine errors. If the actual weights have a mean of 1.05 and standard deviation of 0.04, at what weight does a package fall into the bottom 10%? (Round to 3 decimal places)
0.998 lbs
The weights of a specific breed of puppy are normally distributed with a mean of 12 lbs and a standard deviation of 2 lbs. Use the Empirical Rule to find the weight range that contains the middle 95% of all puppies.
8lbs and 16lbs
The heights of high school basketball players are normally distributed with a mean of 74 inches and standard deviation of 3 inches. What is the probability that a randomly selected player is shorter than 70 inches?
0.09
A lightbulb manufacturer finds that the life of their bulbs follows a normal distribution with a mean of 1,500 hours and a standard deviation of 100 hours. What percentage of bulbs will last longer than 1,650 hours?
0.07
The scores on a standardized test are normally distributed with a mean of 500 and a standard deviation of 100. What is the probability that a student scores between 450 and 625?
0.59
A college only admits students who score in the top 15% on an entrance exam. If the exam scores are normally distributed with mean = 200 and SD = 30, what is the minimum score a student needs to be admitted? (Round 2 decimal places)
231.09