Question

Suppose 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.A) Slect a student at random from university A. Find the probability that the student's IQ is at least 135 points.B) Select a student at random from each school. Find the probability that the university A students IQ is at least 5 points highter than the university B students' IQ.C) Select 3 university B students at random. Find the probability that this group's average IQ is at least 115 points.

Answer 1

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)$P(X>135) = \\P(Z>0.625)\\=0.0266$

B) Since X and Y are independent we have

X-Y is Normal with mean = 140-120 =20 and $Var (x-y)=Var(x)+Var(y) = 19$

$P(X-Y)>5\\\\=1-0.00029\\=0.9997$

C) For a group of 3, average has std deviation = $\frac{11}{\sqrt{3} } \\=6.351$

$P(\bar y >115)\\= P(z>\frac{-5}{6.351} \\=0.7856$