Question

1.) find z to have A=.9831 to the right of z 1B.) the mean of the reading speed of 7th grade students is 125 words per min, and a standard deviation of 24 words per min. what is the reading speed of a student in the 90th percentile? 1C.) what is the probability that a randomly selected 7th grader reads less than 100 words per min?

Answer 1

Solution,

1) Using standard normal table,

P(Z > z) = 0.9831

= 1 - P(Z < z) = 0.9831  

= P(Z < z) = 1 - 0.9831

= P(Z < z ) = 0.0169

= P(Z < -2.12 ) = 0.0169  

z = -2.12

1 B) mean = = 125

standard deviation = = 24

Using standard normal table,

P(Z < z) = 90%

= P(Z < z ) = 0.90

= P(Z < 1.28 ) = 0.90  

z = 1.28

Using z-score formula,

x = z * +

x = 1.28 * 24 + 125

x = 155.72 words per min.

1 C) P(x < 100)

= P[(x - ) / < (100 - 125) / 24]

= P(z < -1.04)

Using z table,

= 0.1492