The normal distribution with a mean of 68 and standard dev

The normal distribution with a mean of ? = 6.8 and standard deviation ? = 1.6 is a good description of the Iowa Test vocabulary scores of seventh-grade students in Gary, Indiana. This is a continuous probability model for the score of a randomly chosen student. The density curve is shown below. Call the score of a randomly chosen student X for short.

What is the probability (0.01) of event \"the student chosen has a score of 9.1 or higher\"?      

The normal distribution with a mean of ? = 6.8 and standard deviation ? = 1.6 is a good description of the Iowa Test vocabulary scores of seventh-grade students in Gary, Indiana. This is a continuous probability model for the score of a randomly chosen student. The density curve is shown below. Call the score of a randomly chosen student X for short. What is the probability (0.01) of event the student chosen has a score of 9.1 or higher?

Solution

Mean = 6.8

Sd=1.6

The distribution is approximately normal, z distribution used.

For x = 9.1, z = (9.1 - 6.8)/1.6 =1.44

P( x >9.1 ) = P( z >1.44) = 0.0749

The required P=0.07    ( two decimals)