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xxTIMURxx [149]
3 years ago
9

Assume that adults have IQ scores that are normally distributed with a mean of mu equals 105 and a standard deviation sigma equa

ls 15. Find the probability that a randomly selected adult has an IQ between 87 and 123.

Mathematics
1 answer:
Sindrei [870]3 years ago
5 0

Answer:

0.7698

Step-by-step explanation:

If you call your random variable X, then what you are looking for is

P(87 \leq X \leq 123)

because you want the probability of X being <em>between 87 and 123.</em>

We need a table with of the normal distribution. But we can only find the table with \mu = 0 and \sigma = 1. Because of that, first we need to  <em>normalize </em>our random variable:

Z = \frac{X - \mu}{\sigma} = \frac{X - 105}{15}

(you can always normalize your variable following the same formula!)

now we can do something similar to our limits, to get a better expression:

\frac{87 - 105}{15} = \frac{-18}{15} = -1.2

\frac{123 - 105}{15} = \frac{18}{15} = 1.2

And we transform our problem to a simpler one:

P(87 \leq X \leq 123) = P(-1.2 \leq Z \leq 1.2) = P(Z \leq 1.2) - P(Z \leq -1.2)

(see Figure 1)

From our table we can see that P(Z \leq 1.2) = 0.8849 (this is represented in figure 2).

Remember that the whole area below the curve is exactly 1. So we can conclude that  P(Z \geq 1.2) = 0.1151 (because 0.8849 + 0.1151 = 1). We also know the normal distribution is symmetric, then

P(Z \leq -1.2)= P(Z \geq 1.2) = 0.1151.

FINALLY:

P(Z \leq 1.2) - P(Z \leq -1.2) = 0.8849 - 0.1151 = 0.7698

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The sum of four consecutive even integers is 180. what is the smallest integer?
n200080 [17]
42
let the smallest even number be x, than the four even numbers are x, x+2, x+4, x+6, their sum is 180

x+x+2+x+4+x+6=180
                4x+12=180
                      4x=168
                        x=42
the smallest even number is 42.

3 0
3 years ago
Consider the sequence of numbers: 3/8, 3/4, 1 /18, 1 1/2, 1 7/8
vredina [299]

Question:

Consider the sequence of numbers: \frac{3}{8}, \frac{3}{4}, 1\frac{1}{8}, 1\frac{1}{2}, 1\frac{7}{8}

Which statement is a description of the sequence?

(A) The sequence is recursive, where each term is 1/4 greater than its preceding term.

(B) The sequence is recursive and can be represented by the function

f(n + 1) = f(n) + 3/8 .

(C) The sequence is arithmetic, where each pair of terms has a constant difference of 3/4 .

(D) The sequence is arithmetic and can be represented by the function

f(n + 1) = f(n)3/8.

Answer:

Option B:

The sequence is recursive and can be represented by the function

f(n + 1) = f(n) + \frac{3}{8}  .

Explanation:

A sequence of numbers are

\frac{3}{8}, \frac{3}{4}, 1\frac{1}{8}, 1\frac{1}{2}, 1\frac{7}{8}

Let us first change mixed fraction into improper fraction.

\frac{3}{8}, \frac{3}{4}, \frac{9}{8}, \frac{3}{2}, \frac{15}{8}

To find the pattern of the sequence.

To find the common difference between the sequence of numbers.

\frac{3}{4}-\frac{3}{8}=\frac{6}{8}-\frac{3}{8}= \frac{3}{8}

\frac{9}{8}-\frac{3}{4}=\frac{9}{8}-\frac{6}{8}= \frac{3}{8}

\frac{3}{2}-\frac{9}{8}=\frac{12}{8}-\frac{9}{8}= \frac{3}{8}

\frac{15}{8}-\frac{3}{2}=\frac{15}{8}-\frac{12}{8}= \frac{3}{8}

Therefore, the common difference of the sequence is 3.

That means each term is obtained by adding \frac{3}{8} to the previous term.

Hence, the sequence is recursive and can be represented by the function f(n + 1) = f(n) + \frac{3}{8}  .

3 0
3 years ago
Factor completely: <br> x^3 - x^2 - 6x
PSYCHO15rus [73]

Answer:

x(x-3)(x+2)

Step-by-step explanation:

1. Find the GCF (Greatest Common Factor)

GCF=x

2. Factor out the GCF and simplify.

x(x^{2} -x-6)

3. Factor x^{2} -x-6.

Which two numbers add up to -1 and multiply to -6?

<u>-3 and 2</u>

Rewrite the expression using the numbers above.

(x-3)(x+2)

4. Done!

x(x-3)(x+2)

4 0
2 years ago
a school had 690 students sign up for the trivia teams if they wanted to have nine teams with the same number of students on eac
Anna11 [10]

Answer:

30 more students

Step-by-step explanation:

690 + 30 = 720

720 / 9 = 80


8 0
3 years ago
What is the sum of the geometric series
Sergio039 [100]
Answer: 2343 / 256

Explanation

I will do this for you in two forms: 1) adding each term, and 2) using the general formula for the sum of geometric series.

1) Adding the terms:

 4
∑ 3 (3/4)^i = 3 (3/4)^0 + 3 (3/4)^1 + 3 (3/4)^2 + 3 (3/4)^3 + 3 (3/4)^4
i=0

= 3 + 9/4 + 27/16 + 81/64 + 243/256 = [256*3 + 27*16 + 64*9 + 4*81 + 243] / 256 =

= 2343 / 256

2) Using the formula:

n-1
∑ A (r^i) = A [1 - r^(n) ] / [ 1 - r]
i=0

Here n - 1 = 4 => n = 5

r = 3/4

A = 3

Therefore the sum is 3 [ 1 - (3/4)^5 ] / [ 1 - (3/4) ] =

= 3 [ 1 - (3^5) / (4^5) ] / [ 1/4 ] = 3 { [ (4^5) - (3^5) ] / (4^5) } / {1/4} =

= (3 * 781) / (4^5) / (1/4) =  3 * 781 / (4^4) = 2343 / 256

So, no doubt, the answer is 2343 / 256
5 0
3 years ago
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