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taurus [48]
1 year ago
7

What is the probability that a random sample of 10 second grade students from the city results in a mean reading rate of more th

an 96 words per​ minute
Mathematics
1 answer:
Vinvika [58]1 year ago
3 0

Using the normal distribution, it is found that there is a 0.1029 = 10.29% probability that the sample mean is above 96.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

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

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
  • By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation s = \frac{\sigma}{\sqrt{n}}.

Researching the problem on the internet, the parameters are given as follows:

\mu = 92, \sigma = 10, n = 10, s = \frac{10}{\sqrt{10}} = 3.1623

The probability that the sample mean is above 96 is <u>one subtracted by the p-value of Z when X = 96</u>, hence:

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

By the Central Limit Theorem:

Z = \frac{X - \mu}{s}

Z = \frac{96 - 92}{3.1623}

Z = 1.265

Z = 1.265 has a p-value of 0.8971.

1 - 0.8971 = 0.1029 = 10.29% probability that the sample mean is above 96.

More can be learned about the normal distribution at brainly.com/question/4079902

#SPJ1

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Solve the inequality 5z+8≥-7
kirza4 [7]

Answer:

z≥−3

Step-by-step explanation:

1 Subtract 88 from both sides.

5z≥−7−8

2 Simplify  -7-8−7−8  to  -15−15.

5z≥−15

3 Divide both sides by 55.  

z≥− 15/5

 

4 Simplify 15/5 to 3

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3 0
3 years ago
Kim decides to give her old toys to her younger cousins. She gives her cousin Sarah 2/3. Then, she gives her cousin Ryan 2/5 of
KatRina [158]

Answer:

30

Step-by-step explanation:

Work backwards:

  • 6 is 3/5 of a number, and that number is 10
  • 10 is 1/3 of a number, and that number is 30

Check your work:

  • 2/3 of 30=20 toy to Sarah
  • 30-20=10 toys left
  • 2/5 of 10=4 toys to Ryan
  • 10-4=6 toys left
3 0
2 years ago
Please help with this question​
vredina [299]

answer:

is that a quiz or a test? cuz if so, brainly doesn't let us do ur work. someone will report. but i wont. dw!

7 0
3 years ago
Read 2 more answers
1. Write as a base with a positive exponent, then evaluate. Write your final answer as a
vodomira [7]

Answer:

Well a base with a positive exponent would be 5^3. All this means is 5x5x5 which is 125.

Step-by-step explanation:

Hope this helps!

5 0
3 years ago
Factor the expression 8x^3y-8x^2y-30xy
miv72 [106K]

Find the Greatest Common Factor (GCF)

GCF = 2xy

Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

2xy(8x^3y/2xy + -8x^2y/2xy + -30xy/2xy)

Simplify each term in parenthesis

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Split the second term in 4x^2 - 4x - 15 into two terms

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Factor out common terms in the first two terms, then in the last two terms;

2xy(2x(2x + 3) -5(2x + 3))

Factor out the common term 2x + 3

<u>= 2xy(2x + 3)(2x - 5)</u>

4 0
3 years ago
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