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alexira [117]
1 year ago
10

WHEN GIVEN A RAW SCORE, EXPLAIN HOW TO USE THE NORMAL CURVE TO COMPARE THAT SCORE TO THE POPULATION. WHAT IS A Z-SCORE?

Mathematics
1 answer:
valina [46]1 year ago
5 0

<span>1. </span>When given a raw score, it must be converted into a z-score (standard score). Raw scores cannot be placed on a normal distribution curve because they do not have the same means and standard deviations, but when it is converted into a z-score, the number of standard deviations above or below the population mean can be measured. The z-scores on the center are average, the scores on the left are lower than average and the scores on the right are higher than average.

<span>2. </span>A z-score is a standard score which can be placed on a normal distribution curve. A z-score indicates the distance of the standard deviations from the mean (center of the curve).

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Answer:

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Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

P(B|A) = \frac{P(A \cap B)}{P(A)}

In which

P(B|A) is the probability of event B happening, given that A happened.

P(A \cap B) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Dressed correctly

Event B: Monday

Probability of being dressed correctly:

100% = 1 out of 4/7(mom dresses).

(0.5)^3 = 0.125 out of 3/7(toddler dresses himself). So

P(A) = 0.125\frac{3}{7} + \frac{4}{7} = \frac{0.125*3 + 4}{7} = \frac{4.375}{7} = 0.625

Probability of being dressed correctly and being Monday:

The toddler dresses himself on Monday, so (0.5)^3 = 0.125 probability of him being dressed correctly, 1/7 probability of being Monday, so:

P(A \cap B) = 0.125\frac{1}{7} = 0.0179

What is the probability that today is Monday?

P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0179}{0.625} = 0.0286

0.0286 = 2.86% probability that today is Monday.

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Evaluate sin(Arcos(-9/√145)).
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Use the fact that \sin x = \sqrt{1-\cos^2 x} to solve it.

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