(a) Find the z-score for an IQ of 111, rounded to three decimal places. (b) Find the probability that the person has an IQ greater than 111. (c) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z-score. Use your z-score from part (a), rounded to one decimal place).

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IQ is normally distributed with a mean of 100 and
a standard deviation of 15. Suppose one
individual is randomly chosen. Let X = IQ of an
individual.
(a) Find the z-score for an IQ of 111, rounded to
three decimal places.
(b) Find the probability that the person has an IQ
greater than 111.
(c) Shade the area corresponding to this
probability in the graph below. (Hint: The x-axis is
the z-score. Use your z-score from part (a),
rounded to one decimal place).
Shade: (Left of a value
. Click and drag the
arrows to adjust the values.
-1.5
(d) MENSA is an organization whose members
have the top 2% of all IQs. Find the minimum IQ
needed to qualify for the MENSA organization.
(e) Sketch the graph, and write the probability
statement.
Transcribed Image Text:IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual. (a) Find the z-score for an IQ of 111, rounded to three decimal places. (b) Find the probability that the person has an IQ greater than 111. (c) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z-score. Use your z-score from part (a), rounded to one decimal place). Shade: (Left of a value . Click and drag the arrows to adjust the values. -1.5 (d) MENSA is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the MENSA organization. (e) Sketch the graph, and write the probability statement.
Expert Solution
Step 1

Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved.

(a)

The random variable X is defined as the IQ of an individual. The mean is 100 and standard deviation is 15. That is, μ=100,σ=15.

The z-score for an IQ of 111 is,

z=x-μσ=111-10015=1115=0.733

Thus, the z-score for an IQ of 111 is 0.733.

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