# Suppose that scores on a particular test are normally distributed with a mean of 140 and a standard

###### Question:

## Answers

The minimum score needed to be in the top 5% of the scores on the test is 172.9.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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:

[tex]\mu = 140, \sigma = 20[/tex]

What is the minimum score needed to be in the top 5% of the scores on the test?

The 100-5 = 95th percentile, which is the value of X when Z has a pvalue of 0.95. So it is X when Z = 1.645.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.645 = \frac{X - 140}{20}[/tex]

[tex]X - 140 = 20*1.645[/tex]

[tex]X = 172.9[/tex]

The minimum score needed to be in the top 5% of the scores on the test is 172.9.

the minimum score needed to be in the top 5% of the scores on the test is 173

Step-by-step explanation:

Suppose that scores on the particular test are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = scores on the test.

µ = mean score

σ = standard deviation

From the information given,

µ = 140

σ = 20

The probability value for the minimum score needed to be in the top 5% of the scores on the test would be (1 - 5/100) = (1 - 0.05) = 0.95

Looking at the normal distribution table, the z score corresponding to the probability value is 1.65

Therefore,

1.65 = (x - 140)/20

Cross multiplying by 20, it becomes

1.65 × 20 = x - 140

33 = x - 140

x = 33 + 140

x = 173

answer: 59

step-by-step explanation:

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒[tex]y=\frac{+1}{+1}x+0[/tex]

or [tex]y=\frac{-1}{-1}x+0[/tex]

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.