Question

Suppose SAT reading scores are normally distributed with a mean of 496 and a standard deviation of 109. The University plans towards scholarships for students who scores are in the top 7%. What is the minimum score required for the scholarship round your answer to the nearest whole number.

278

likes
1389 views

Answer to a math question Suppose SAT reading scores are normally distributed with a mean of 496 and a standard deviation of 109. The University plans towards scholarships for students who scores are in the top 7%. What is the minimum score required for the scholarship round your answer to the nearest whole number.

Expert avatar
Sigrid
4.5
114 Answers
To find the minimum score required for the top 7% of SAT reading scores, you can use the z-score formula. The z-score represents how many standard deviations a particular score is from the mean in a normal distribution. The formula for the z-score is given by:\[ Z = \frac{(X - \mu)}{\sigma} \] Where: - X is the raw score, - μ is the mean of the distribution, - σ is the standard deviation. In this case, you want to find the z-score corresponding to the top 7%, which means finding the z-score that leaves 7% in the tail. You can find this value using a standard normal distribution table or a calculator. For the top 7%, you would look up the z-score that corresponds to the cumulative probability of 0.93 (since 100% - 7% = 93%). Using a standard normal distribution table or calculator, you find that \( Z \approx 1.44 \). Now, plug this z-score back into the z-score formula to find the corresponding raw score (X):\[ 1.44 = \frac{(X - 496)}{109} \] Solve for X : \[ X = 1.44 \times 109 + 496 \] \[ X = 642.96 \] Rounding to the nearest whole number, the minimum score required for the scholarship is 643.

Frequently asked questions (FAQs)
What is the area of a triangle with base 10 cm and height 15 cm?
+
Math question: What is the measure of an angle formed by a tangent and a chord intersecting at a point on the circle?
+
What is the condition for the signs of equality for triangles? Is it
+
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?
2.3/-71.32
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
3/9*4/8=
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.