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3 years ago

WILL MARK BRAINLEIST HURRY

Mathematics

2 answers:

Luden [163]3 years ago

6 0

Answer:

The IQR is the best measurement of spread for games and movies.

Step-by-step explanation:

I took the test

iren [92.7K]3 years ago

4 0

Answer:

Hello, The answer it's D.

Step-by-step explanation:

Assume that the data for both movies and basketball games are normally distributed.

Therefore, the median and the mean are assumed equal.

The standard deviation, σ, is related to the interquartile range by

IQR = 1.35

From the data, we can say the following:

Movies:

Range = 150 - 60 = 90 (approx)

Q1 = 62 (approx), first quartile

Q3 = 120 (approx), third quartlie

Q2 (median) = 90 (approx)

IQR = Q3 - Q1 = 58

σ = IQR/1.35 = 58/1.35 = 43

Basketball:

Range = 150 - 90 = 60 approx

Q1 = 95 (approx)

Q3 = 145 (approx)

Q2 = 125 (approx)

IQR = 145 - 95 = 50

σ = 50/1.35 = 37

Test the given answers.

A. The IQRs are approximately equal, so they are not good measures of spread. This is not a good answer.

B. The std. deviation is a better measure of spread for basketball. This is not a good answer.

C. IQR is not a better measure of spread for basketball games. This is not a good answer.

D. The standard deviation is a good measure of spread for both movies and basketball. This is the best answer.

Answer: D

Have a Great Day!

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A math professor notices that scores from a recent exam are normally distributed with a mean of 61 and a standard deviation of 8

Alexeev081 [22]

Answer:

a) 25% of the students exam scores fall below 55.6.

b) The minimum score for an A is 84.68.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 61 and a standard deviation of 8.

This means that $\mu = 61, \sigma = 8$

(a) What score do 25% of the students exam scores fall below?

Below the 25th percentile, which is X when Z has a p-value of 0.25, that is, X when Z = -0.675.

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

$-0.675 = \frac{X - 61}{8}$

$X - 61 = -0.675*8$

$X = 55.6$

25% of the students exam scores fall below 55.6.

(b) Suppose the professor decides to grade on a curve. If the professor wants 0.15% of the students to get an A, what is the minimum score for an A?

This is the 100 - 0.15 = 99.85th percentile, which is X when Z has a p-value of 0.9985. So X when Z = 2.96.

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

$2.96 = \frac{X - 61}{8}$