Respuesta :
Answer:
0.0266, 0.9997,0.7856
Step-by-step explanation:
Given that the IQs of university​ A's students can be described by a normal model with mean 140 and standard deviation 8 points. Also suppose that IQs of students from university B can be described by a normal model with mean 120 and standard deviation 11. Let x be the score by A students and Y the score of B.
A)[tex]P(X>135) = \\P(Z>0.625)\\=0.0266[/tex]
B) Since X and Y are independent we have
X-Y is Normal with mean = 140-120 =20 and [tex]Var (x-y)=Var(x)+Var(y) = 19[/tex]
[tex]P(X-Y)>5\\\\=1-0.00029\\=0.9997[/tex]
C) For a group of 3, average has std deviation = [tex]\frac{11}{\sqrt{3} } \\=6.351[/tex]
[tex]P(\bar y >115)\\= P(z>\frac{-5}{6.351} \\=0.7856[/tex]
The probability of the student's IQ being at least 135 points, university A student's IQ is at least 5 points higher than the university B students' IQ and the group's average IQ is at least 115 points are 0.0266, 0.9997, and 0.7856.
What is probability?
Probability means possibility. It deals with the occurrence of a random event.
Given
Suppose that the IQs of university A's students can be described by a normal model with a mean of 140 and a standard deviation of 8 points.
Also, suppose that IQs of students from university B can be described by a normal model with a mean of 120 and a standard deviation of 11.
Let x be the score by A students and y be the score of B.
A) Select a student at random from university A. The probability of the student's IQ is at least 135 points.
[tex] P(x> 135) = P(z) > 0.625 = 0.0266 [/tex]
B) The student at random from each school. Then the probability that the university A student's IQ is at least 5 points higher than the university B students' IQ.
[tex] var(x-y) = var(x) + var(y) = 19 \\\\P(x-y)>5 [/tex]
Then
[tex] P(x-y) > 5 \\\\ =1-0.00029 \\\\ = 0.9997 [/text]
C) Select 3 university B students at random. Then the probability that this group's average IQ is at least 115 points.
[tex] P(\ber{y} > 115) = P(z > \dfrac{-5}{6.351}) \\\\ P(\ber{y} > 115) = 0.7856 [/tex]
More about the Probability link is given below.
https://brainly.com/question/795909
