z-Scores and Area under the Curve

Question

z-Scores and Area under the Curve
A researcher collected data on adults using an intelligence test. The data for these adults were approximately normally distributed with the following mean and standard deviation		mean = 9999 points	standard deviation = 1818 points		Use this information and the online normal distribution calculator to answer the questions below. Round your percents to two decimal places.		Note: Use z-scores rounded to 2 decimal places and the standard normal distribution to avoid roundoff errors.
Normal Calculator
If an adult is randomly selected from the study, what is the probability the adult scored between 110110 points and 127127 points? %
If an adult is randomly selected from the study, what is the probability the adult scored less than 103.3103.3 points? %
If an adult is randomly selected from the study, what is the probability the adult scored more than 133.4133.4 points? %
If an adult is randomly selected from the study, what is the probability the adult scored less than 56.756.7 points or more than 144.1144.1 points? %

Answer 1

P(110<x<127) = P((121-99)/18)<z<(127-99)/18))

= 0.2115 = 21.15%

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P((56.7>x) and (144.1<x)) = P((56.7-99)/18>z) + P((144.1-99)/18<z)

= 0.0155 = 1.55%