Non Standard Distributions, Central Limit Theorem

Question

Find the area of the shaded region. The graph to the right depicts IQ scores of​ adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

102

122

1. 
   
2. 
   
3. 
   

A symmetric bell-shaped curve is plotted over a horizontal scale. Two vertical lines run from the scale to the curve at labeled coordinates 102 and 122, which are both to the right of the curve’s center and peak. The area under the curve between the vertical lines is shaded.

Question content area bottom

Part 1

The area of the shaded region is

enter your response here.

​(Round to four decimal places as​ needed.)

Answer 1

Area of the shaded region = P(102 < X < 122)

Using the TI-83, 83+, 84, 84+ Calculator to calculate normal probabilities

Go to 2nd DISTR, and select item 2: normalcdf.

The syntax is: normalcdf (lower bound, upper bound, mean, standard deviation).

So, area of the shaded region

= P(102 < X < 122)

= normalcdf(102, 122, 100, 15)

= 0.3757