Hi

Population: mean is 500 and the deviation is 100.

P(400 ≤  x ≤ 600) = P(-1 ≤  z ≤ 1) = P(z ≤ 1) - P(z ≤ -1) = .8413 - .1587 = .6826



For the normal distribution: Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  

Area under the standard normal curve to the left of the particular z is P(z)

Note: z = 0 (x value: the mean) 50% of the area under the curve is to the left and 50%  to the right





one  standard deviation from the mean accounts for about 68% of the set 

two standard deviations from the mean account for about 95%

and three standard deviations from the mean account for about 99.7%.

 

RELATED QUESTIONS

Is 120.5 correct? A standardized test has a mean of 600 and a standard deviation of 75.... (answered by stanbon)

A standardized test is designed so that the scores are normally distributed with a mean... (answered by dfrazzetto)

A standardized test has a mean of 600 and a standard deviation of 75. If 1000 students... (answered by stanbon)

I am stuck :(

The distribution of scores on a standardized aptitude test is... (answered by ad_alta)

The distribution of scores on a standardized aptitude test is approximately normal with a  (answered by Boreal)

The distribution of scores on a standardized aptitude test is approximately normal with a  (answered by Boreal)

A standardized IQ test provides a normal distribution of scores with a mean of 100 and a... (answered by ewatrrr)

How do I solve the following problem based on the formula, Z = (x-m)/sd

The graduate... (answered by stanbon)

The graduate selection committe wants to select the top 10% of applicants. On a... (answered by stanbon)