SOLUTION: On a standardized test with a normal distribution the mean is 500 and the deviation is 100. If 1000 people took the test approximately how many would theoretically score between 40

 

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%.