Respuesta :
Answer:
(a) The percentage of people having an IQ score between 67 and 133 is 99.73%.
(b) The percentage of people having an IQ score less than 89 or greater than 111 is 31.73%.
(c) The percentage of people having an IQ greater than 111 is 15.87%.
Step-by-step explanation:
The random variable X can be defined as the scores of an IQ test.
The random variable X is normally distributed with parameters μ = 100 and σ = 11.
(a)
Compute the probability of people who has an IQ score between 67 and 133 as follows:
[tex]P(67<X<133)=P(\frac{67-100}{11}<\frac{X-\mu}{\sigma}<\frac{133-100}{11})\\\\=P(-3<Z<3)\\\\=P(Z<3)-P(Z<-3)\\\\=0.99865-0.00135\\\\=0.9973[/tex]
The percentage is, 0.9973 × 100 = 99.73%.
Thus, the percentage of people having an IQ score between 67 and 133 is 99.73%.
(b)
Compute the probability of people having an IQ score less than 89 or greater than 111 as follows:
[tex]P(X<89\ \cup\ X>111)=1-P(89<X<111)\\\\=1-P(\frac{89-100}{11}<\frac{X-\mu}{\sigma}<\frac{111-100}{11})\\\\=1-P(-1<Z<1)\\\\=1-[P(Z<1)-P(Z<-1)]\\\\=1-[0.84134-0.15866]\\\\=0.31732\\\\\approx 0.3173[/tex]
The percentage is, 0.3173 × 100 = 31.73%.
Thus, the percentage of people having an IQ score less than 89 or greater than 111 is 31.73%.
(c)
Compute the probability of people having an IQ score greater than 111 as follows:
[tex]P(X>111)=P(\frac{X-\mu}{\sigma}>\frac{111-100}{11})\\\\=P(Z>1)\\\\=1-P(Z<1)\\\\=1-0.84134\\\\=0.15866\\\\\approx 0.1587[/tex]
The percentage is, 0.1587 × 100 = 15.87%.
Thus, the percentage of people having an IQ greater than 111 is 15.87%.
The % of people having an IQ score between the 67 and the 133 is 99.73%. The % of people having an IQ score less than the 89 or greater than 111 is 31.73%. The % of people having an IQ greater than 111 is 15.87%.
What is the percentage of the scope of the IQ test.?
As per the IQ test which is done to check the intelligent quotient of a score that s derived from a standard sets of tests. They are made to test human intelligence. The IQ score falls in a bell-shaped curve with the distortion of 100 and SD of 11.
The percentage of the people having a score between the 67 and 133 was 099.7% and those between the 89 of more 111 is 31.7% and those having a greater IQ of 111 are 15.8 % that is declining to the top.
Find out more information about the IQ test.
brainly.com/question/2748723.
