A standard I.Q. test produces normally distributed results with a mean of 104 and a standard deviation of 16 for 52,000 students
2 answers:
The IQ scores are RVs (X) normally distributed with mean and standard deviation
.
The probability is calculated after converting the raw score to the standard score,
.
Now use normal distribution table or technology,
.
Thus, the number of people who would have I.Q.s below 76 out of 52,000 is
.
Therefore, the approximate number is .
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Let, the numbers be "x" and "y". Consider "x" as the triple digit number.
Now, according to the question,
x + y = 217..........................equation (1)
x * y = 642............................equation (2)
Now,
Taking equation (2),
x * y = 642
y = 642 / x..................................equation (3)
Now, Taking equation (1),
Substituting the value of y from equation (3), we get,
Using zero product property,
EITHER,
x - 3 = 0
x = 3
OR,
x - 214 = 0
x = 214
Since, "x" is the triple digit number, x = 214.
Now,
Taking equation (2),
x * y = 642
Substituting the value of "x" in the equation, we get,
(214) * y = 642
y = 642 / 214
y = 3
So, the numbers are 214 and 3.
Now, according to the question,
x + y = 217..........................equation (1)
x * y = 642............................equation (2)
Now,
Taking equation (2),
x * y = 642
y = 642 / x..................................equation (3)
Now, Taking equation (1),
Substituting the value of y from equation (3), we get,
Using zero product property,
EITHER,
x - 3 = 0
x = 3
OR,
x - 214 = 0
x = 214
Since, "x" is the triple digit number, x = 214.
Now,
Taking equation (2),
x * y = 642
Substituting the value of "x" in the equation, we get,
(214) * y = 642
y = 642 / 214
y = 3
So, the numbers are 214 and 3.