Mathematics, 26.03.2020 22:20 montgomerykarloxc24x

In a recent year, students taking a mathematics assessment test had a mean of 290 and a standard deviation of 37. Possible test scores could range from 0 to 500. (hint: use 0 as the lower limit and 500 as the upper limit) [4 pts. Each] a) Find the probability that a student had a score less than 320. b) Find the probability that a student had a score between 250 and 300. c) What percent of the students had a test score greater than 200? d) What is the lowest score that would still place a student in the top 5% of the scores? e) What is the highest score that would still place a student in the bottom 25% of the scores

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Answer from: amourrrblackkkk

a) 79.10% probability that a student had a score less than 320.

b) 46.63% probability that a student had a score between 250 and 300.

c) 99.25% of the students had a test score greater than 200

d) 350.865

e) 265.025

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:

$\mu = 290, \sigma = 37$

a) Find the probability that a student had a score less than 320.

This is the pvalue of Z when X = 320. So

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

$Z = \frac{320 - 290}{37}$

Z = 0.81

Z = 0.81 has a pvalue of 0.7910

79.10% probability that a student had a score less than 320.

b) Find the probability that a student had a score between 250 and 300.

This is the pvalue of Z when X = 300 subtracted by the pvalue of Z when X = 250.

X = 300

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

$Z = \frac{300 - 290}{37}$

Z = 0.27

Z = 0.27 has a pvalue of 0.6064

X = 250

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

$Z = \frac{250 - 290}{37}$

Z = -1.08

Z = -1.08 has a pvalue of 0.1401

0.6064 - 0.1401 = 0.4663

46.63% probability that a student had a score between 250 and 300.

c) What percent of the students had a test score greater than 200?

This is 1 subtracted by the pvalue of Z when X = 200. So

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

$Z = \frac{200 - 290}{37}$

Z = -2.43

Z = -2.43 has a pvalue of 0.0075

1 - 0.0075 = 0.9925

99.25% of the students had a test score greater than 200

d) What is the lowest score that would still place a student in the top 5% of the scores?

X when Z has a pvalue of 1-0.05 = 0.95. So X when Z = 1.645.

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

$1.645 = \frac{X - 290}{37}$

X - 290 = 37*1.645

X = 350.865

e) What is the highest score that would still place a student in the bottom 25% of the scores

X when Z has a pvalue of 0.25. So X when Z = -0.675

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

$-0.675 = \frac{X - 290}{37}$

X - 290 = 37*(-0.675)

X = 265.025

Answer from: Quest

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

Answer from: Quest

hello i am doing good for you that it's summer in your country or state ; )

btw in my country we just have sun and rain as (because i live in the caribbean lol)

also, thx a lot for the points : )

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In a recent year, students taking a mathematics assessment test had a mean of 290 and a standard dev...