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Lisa [10]
2 years ago
13

IQ scores are normally normally distributed with a mean of 100 and center deviation of 15 if one person is randomly selected wha

t is the probability that the persons IQ far between 110 and 130
Mathematics
1 answer:
Arlecino [84]2 years ago
6 0

Answer:

22.86% probability that the persons IQ is between 110 and 130

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 100, \sigma = 15

If one person is randomly selected what is the probability that the persons IQ is between 110 and 130

This is the pvalue of Z when X = 130 subtracted by the pvalue of Z when X = 110.

X = 130

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

Z = \frac{130 - 100}{15}

Z = 2

Z = 2 has a pvalue of 0.9772

X = 110

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

Z = \frac{110 - 100}{15}

Z = 0.67

Z = 0.67 has a pvalue of 0.7486

0.9772 - 0.7486 = 0.2286

22.86% probability that the persons IQ is between 110 and 130

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A man standing on a lighthouse at a height of 124 feet sights two boats directly in front of him. One is at an angle of depressi
Ksivusya [100]

Answer:

125\ ft

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

In the right triangle ABC find the length side BC

we know that

tan(62\°)=\frac{124}{BC}

BC=\frac{124}{tan(62\°)}

step 2

In the right triangle ABD find the length side BD

we know that

tan(33\°)=\frac{124}{BD}

BD=\frac{124}{tan(33\°)}

step 3

we know that

The distance between the two boats is the length side CD

CD=BD-BC

substitute the values  

CD=\frac{124}{tan(33\°)}-\frac{124}{tan(62\°)}=125\ ft

5 0
3 years ago
I need the answer to a parts I-iii and the answer to b
fomenos

Answer:

a)

i) Mean = 72

ii) Median = 72

iii) Mode = 72

b)

69, 70, 71, 72, 72, 72, 73, 74, 75

Step-by-step explanation:

<u>a. To find mean, median and mode</u>

It is given that all the 9 students get 72 marks.

Therefore the data set be,

72, 72, 72, 72, 72, 72, 72, 72 72

<u>i) mean </u>= (sum of data)/(total number of data)

 = (9 * 72)/9 = 9

<u>ii) Median </u>- Central data in the data set when arranging ascending or descending order

72, 72, 72, 72, 72, 72, 72, 72 72

Median = 72

<u>iii) Mode </u>- Most repeating data in the data set

Here mode = 72

<u>b). To find a data set</u>

69, 70, 71, 72, 72, 72, 73, 74, 75

Here Mean, mode and median are all 72

3 0
3 years ago
12 times 13 equals what
Inessa [10]
It equal 156. hope it helps
7 0
2 years ago
Read 2 more answers
An open box is to be made out of a 12-inch by 20-inch piece of cardboard by cutting out squares of equal size from the four corn
Natali5045456 [20]

Answer:

Length = 15.14, width = 7.14 and height = 2.43  inches.

( correct to the nearest hundredth).

Step-by-step explanation:

Let the lengths of the squares cut out be x inches.

Then the width of the box will be 12 - 2x and the length will be

20 - 2x inches.

The height of the box is x inches.

Volume V = x(20-2x)(12-2x)

To find the value of x when V is a maximum we find the derivative and equate it to zero.

V = x( 240 - 64x + 4x^2)

V = 4x^3 - 64x^2 + 240x

dV/dx = 12x^2 - 128x + 240 = 0

4(3x^2 - 32x + 60) = 0

This won't factor so we use the formula:

x = [-(-32) +/- √((-32)^2 - 4*3*60)] / 6

= 8.24, 2.43.

So one of these gives a maximum Volume.

The second derivative

d^2V/dx^2 = 24x - 128

When x = 8.24,  this = 69.6 (positive) so this gives a minimum.

x = 2.43 gives a negative  value ( -49.7)  so this is the maximum

So the dimensions are:-

length = 20 - 2(2.43) = 15.14

width = 12 - 2(2.43) = 7.14

height = 2.43.

7 0
2 years ago
What is the value of x in inches ?
Marysya12 [62]

Answer:

it really depends on what the question is.

Step-by-step explanation:

4 0
3 years ago
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