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skad [1K]
3 years ago
13

The scores for a certain test of intelligence are normally distributed with mean 85 and standard deviation 11. Find the 90th per

centile of these scores.
Mathematics
1 answer:
jonny [76]3 years ago
5 0

Answer:

99.1 is the 90th percentile of these scores.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 85

Standard Deviation, σ = 11

We are given that the distribution of score is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

We have to find the value of x such that the probability is 0.90

P( X < x) = P( z < \displaystyle\frac{x - 85}{11})=0.90  

Calculation the value from standard normal z table, we have,  

P(z \leq 1.282) = 0.90

Putting values, we get,

\displaystyle\frac{x - 85}{11} = 1.282\\\\x = 99.1

Thus, 99.1 is the 90th percentile of these scores.

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A machine is used to fill Apple Juice bottles with juice. The machine has a known standard deviation of σ = 0.05 liters. The tar
Lina20 [59]

Answer:

The probability that the quality control manager will shut down the machine is 0.0002.

Step-by-step explanation:

We are given that a machine is used to fill Apple Juice bottles with juice. The machine has a known standard deviation of σ = 0.05 liters. The target mean fill volume is µ = 2.0 liters.

A quality control manager obtains a random sample of 50 bottles. He will shut down the machine if the sample of these 50 bottles is less than 1.95 or greater than 2.1.

<u><em>Let </em></u>\bar X<u><em> = sample mean fill volume</em></u>

The z score probability distribution for sample mean is given by;

                               Z  = \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \mu = population mean fill volume = 2 liters

           \sigma = standard deviation = 0.05 liters

           n = sample of bottles = 50

Now, it is provided that he will shut down the machine if the sample of these 50 bottles is less than 1.95 or greater than 2.1.

  • So, Probability that the sample of these 50 bottles is less than 1.95 is given by = P(\bar X < 1.95)

         P(\bar X < 1.95) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < \frac{1.95-2}{\frac{0.05}{\sqrt{50} } } ) = P(Z < -7.07) = 1 - P(Z \leq 7.07)

                                                         = 1 - 0.9999 = 0.0001

  • Probability that the sample of these 50 bottles is greater than 2.1 is given by = P(\bar X > 2.1)

        P(\bar X > 2.1) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } > \frac{2.1-2}{\frac{0.05}{\sqrt{50} } } ) = P(Z > 14.14) = 1 - P(Z < 14.14)

                                                     = 1 - 0.9999 = 0.0001

Because the highest critical value in the z table is given as x = 4.40 for area of 0.99999.

Therefore, probability that the quality control manager will shut down the machine = 2 \times 0.0001 = 0.0002.

4 0
3 years ago
What is the linear equation for this graph? (y=mx+b)
mart [117]

Answer:

y = -3x - 3

Step-by-step explanation:

the y-intercept is -3 as shown in the graph, so, b = -3

if you count, the rise is 3 and the run is -1, so the slope will be -3/1

-3/1 equals to -3

y = -3x - 3

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3 years ago
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Y=t+12 this is one the answers
7 0
3 years ago
I need help please!!!
tangare [24]

Answer:

it's yes

Step-by-step explanation:

3 0
3 years ago
11. Explain how to evaluate the expression 9 +(45 x 2) = 10.
Dmitry_Shevchenko [17]

The Answer Is 18

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45x2=90

The next thing you must do is divide 90 by 10 since division is before addition.

90/10=9

Now combine like terms.

9+9=18

7 0
3 years ago
Read 2 more answers
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