$MathMaster logo$

MathMaster

Home
general
several intelligence tests gave a score that follows a normal law with mean 100 and standard deviation 15 determine the pe

Question

Several intelligence tests gave a score that follows a normal law with mean 100 and standard deviation 15. Determine the percentage of the population that would obtain a coefficient between 95 and 110.

210

likes

1049 views

Answer to a math question Several intelligence tests gave a score that follows a normal law with mean 100 and standard deviation 15. Determine the percentage of the population that would obtain a coefficient between 95 and 110.

$Expert avatar$

4.6

97 Answers

\text{1. Convert the raw scores to the standard normal variable Z:}

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

\text{For X = 95:}

Z = \frac{95 - 100}{15} = -\frac{1}{3}

\text{For X = 110:}

Z = \frac{110 - 100}{15} = \frac{2}{3}

\text{2. Find the probability for these Z values using the standard normal distribution table:}

P(Z

P(Z

\text{3. Compute the difference to find the percentage of the population within this score range:}

P(-\frac{1}{3}

P(-\frac{1}{3}

\text{Therefore, the percentage of the population that would obtain a coefficient between 95 and 110 is 37.81\%}

Frequently asked questions (FAQs)

What is the conversion of 150 degrees to radians?

+

What is the value of f(x)=c, where c is a constant number, when x is any real number?

+

What is the equation to find the missing value if the median of a set with even number of terms is 10 and the middle two terms are 8 and 12?

+

New questions in Mathematics

Calculate to represent the function whose graph is a line that passes through the points (1,2) and (−3,4). What is your slope?

A circular park has a diameter of 150ft. A circular fence is to be placed on the edge of this park. Calculate the cost of fencing this park if the rate charged is $7 per foot. Use π = 3.14.

10.Silvana must knit a blanket in 9 days. Knitting 8 hours a day, at the end of the fifth day, only 2/5 of the blanket was done. To be able to finish on time, how many hours will Silvana have to knit per day?

(x^2+3x)/(x^2-9)=

A hotel in the Algarve had to offer 1 week of vacation to one of its employees as an Easter gift in a random choice. It is known that 80 people work in this hotel unit, 41 of whom are Portuguese and 39 are foreign nationals. There are 14 Portuguese men and 23 foreign women. Using what you know about conditional probability, check the probability that the gift was offered to a Portuguese citizen, knowing that it was a woman.

The director of a company must transfer 6 people from the human resources department to the sales department, in order to sustain sales during the month of December. What is the probability that he will transfer only 2 of them?

Let r: x - y 5 = 0. Determine a general equation of the line s parallel to the line r, which forms an isosceles triangle with area 8 with the line x = 5 and the Ox axis.

Find all real numbers x that satisfy the equation \sqrt{x^2-2}=\sqrt{3-x}

reduce the expression (7.5x 12)÷0.3

Convert 9/13 to a percent

Use linear approximation to estimate the value of the sine of 31o.

The points (-5,-4) and (3,6) are the ends of the diameter of the circle calculate subequation

Give an example of a function defined in R that is continuous in all points, except in the set Z of integers.

Determine the Linear function whose graph passes through the points (6, -2) and has slope 3.

Given the word WEIRD, determine a four-letter offspring that can be formed with the letters of the word written above

a) Statistics scores are normally distributed with the mean of 75 and standard deviation of 7. What is the probability that a student scores between 80 and 88

8/9 divided by 10/6

In a cheese factory, one pie costs 3800 denars. The fixed ones costs are 1,200,000 denars, and variable costs are 2,500 denars per pie. To encounter: a) income functions. profit and costs; b) the break-even point and profit and loss intervals.