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 result of factoring the mixed number 3 1/2 and multiplying it by the real number 2.7?
+
What are the key features of the graph of the exponential function y = 2^x?
+
What is the range of the data set {12, 15, 18, 21, 25}? The range is the maximum difference between any two numbers.
+
New questions in Mathematics
𝑦 = ( 𝑥2 − 3) (𝑥3 + 2 𝑥 + 1)
a ferry travels 1/6 of the distance between two ports in 3/7 hour. The ferry travels at a constant rate. At this rate, what fraction of the distance between the two ports can the ferry travel in one hour.
Revenue Maximization: A company sells products at a price of $50 per unit. The demand function is p = 100 - q, where p is the price and q is the quantity sold. How many units should they sell to maximize revenue?
Find the equation of the normal to the curve y=x²+4x-3 at point(1,2)
3(4×-1)-2(×+3)=7(×-1)+2
A car that starts from rest moves for 11 min, reaching a speed of 135 km/h, calculate the acceleration it had
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?
Margin of error E=0.30 populations standard deviation =2.5. Population means with 95% confidence. What I the required sample size (round up to the whole number)
The function g:Q→Q is a ring homomorphism such that g(3)=3 and g(5)=5. What are the values of g(8) and g(9)?
15/5+7-5
The thermal representation f(x) = 20 times 0.8 to the power of x is known from an exponential function f. Specify the intersection point with the y-axis
7=-4/3y -1
In an audience of 4000 people, 2 people are chosen, at random, to appear on stage. How many ways can the people be chosen?
What is 75 percent less than 60
a survey showed that 3 out of 7 voters would vote in an election. based on this survey, how many people would vote in a city with 25,000 people?
nI Exercises 65-68, the latitudes of a pair of cities are given. Assume that one city si directly south of the other and that the earth is a perfect sphere of radius 4000 miles. Use the arc length formula in terms of degrees to find the distance between the two cities. 65. The North Pole: latitude 90° north Springfield, Illinois: latitude 40° north
A person runs 175 yards per minute write a variable that represents the relationship between time and distance
Find the equation of a straight line that has slope 3 and passes through the point of (1, 7) . Write the equation of the line in general forms
A triangle is cut by a line s parallel to the base in such a way that it divides the side of the triangle into parts in the ratio of 2 : 3. Find the other side of the triangle if it is known that the line s divides it into parts whose length is 5 cm.
23,456 + 3,451