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trapecia [35]
3 years ago
13

The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard devia

tion of 2 points. For this question, DO NOT apply the standard deviation rule.
(a) What proportion of the students scored at least 19 points on this test, rounded to five decimal places?

(b) What is the 85 percentile of the distribution of test scores, rounded to three decimal places?
Mathematics
1 answer:
maksim [4K]3 years ago
7 0

6.68% of the students scored at least 19 points on this test while the 85 percentile has a test score of 24.08 points

The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

z=\frac{x-\mu}{\sigma} \\\\where\ \mu=mean.\sigma=standard\ deviation, x=raw\ score\\\\Given\ that\ mean(\mu)=22,standard \ deviation (\sigma)=2\\\\For\ x>19:\\\\z=\frac{22-19}{2}=1.5

P(x > 19) = P(z > 1.5) = 1 - P(z < 1.5) = 1 - 0.9332 = 0.0668

6.68% of the students scored at least 19 points on this test

b) 85 percentile corresponds to a z score of 1.04

z=\frac{x-\mu}{\sigma}\\\\1.04 =\frac{x-22}{2} \\\\2.08=x-22\\\\x=24.08

The 85 percentile has a test score of 24.08

Find out more at: brainly.com/question/25012216

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What is the additive inverse of 16 5/7 ? A.-16 7/5 B..-16 5/7 C.16 7/5 D. -16
Reil [10]

Answer:-16 5/7

Step-by-step explanation:

To find the additive inverse of 16 5/7

We get

-16 5/7

7 0
3 years ago
Ja'Von kicks a soccer ball into the air. The function f(x) = –16(x – 2)2 + 64 represents the height of the ball, in feet, as a f
Dima020 [189]

Answer:

The maximum height the ball reaches is 64 feet

Step-by-step explanation:

The given function is f(x) = -16·(x - 2)² + 64

From the equation, the path described by the ball is an inverted n-shaped parabola

The maximum height is therefore, the tip of the parabola

At the maximum height, the slope = 0 because the tip is momentarily flat

Since the slope (y₂ - y₁)/(x₂ - x₁)  = The derivative Δy/Δx, we find the derivative of the function and equate it to zero to find the coordinates at the  maximum height

Δy/Δx = dy/dx = d(-16·(x - 2)² + 64)/dx = -32·(x - 2) = -32·x + 64

To check if it is a maximum, we have;

d²y/dx² = d(-32·x + 64)/dx = -32 which is negative, indicating that the slope is reducing and we at the maximum point of the slope

Therefore for the maximum height Δy/Δx = dy/dx = -32·x + 64 = 0

64 = 32·x

x = 64/32 = 2 seconds

We now have the x-value at the slope, the f(x) value, is therefore;

f(2) = -16·(2 - 2)² + 64 = 64 feet

Therefore, the maximum height the ball reaches is 64 feet.

3 0
3 years ago
Please help me out!!!!!
vekshin1

Answer:

sorry that was my brother

6 0
3 years ago
Anybody know please help
Reil [10]

Answer:

ok

Step-by-step explanation:

1

5 0
3 years ago
7 pints and 9 cups equals how many pints
erik [133]

Answer:

Altogether this would equal 11 1/2 pints

<em>Hope this helped!! Have a god day c;</em>

Step-by-step explanation:


5 0
3 years ago
Read 2 more answers
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