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Lina20 [59]
3 years ago
14

Tyrell's SAT math score was in the 64th percentile. If all SAT math scores are normally distributed with a mean of 500 and a sta

ndard deviation of 100, what is Tyrell's math score? Round your answer to the nearest whole number
Mathematics
1 answer:
jarptica [38.1K]3 years ago
8 0

Answer:

P(x < 535.8) = 0.64

P_{64} = 535.8

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 500

Standard Deviation, σ = 100

We are given that the distribution of SAT 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 0.64

P(X<x) = 0.64

P( X < x) = P( z < \displaystyle\frac{x - 500}{10})=0.64  

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

\displaystyle\frac{x - 500}{100} = 0.358\\x = 535.8

P(x < 535.8) = 0.64

P_{64} = 535.8

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1 1/12-7/10 greater than 1/2 or less than 1/2
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A group of people went to a coffee shop.
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Answer:

Fraction of the people chose a tart = \frac{13}{45}

Step-by-step explanation:

Given - A group of people went to a coffee shop. Each person chose a

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            people who chose a muffin number of people who chose a tart =    

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            : number of people who chose a tart = 5:1.

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Proof -

Let the Total number of People went to a coffee shop = 5x

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As given, number of people who chose coffee: number of people who chose tea = 1:4

⇒Total number of people who chooses coffee = \frac{1}{5}.5x = x

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Now,

As given,

Of those who choose coffee,  number of people who chose a muffin number of people who chose a tart = 2:7

⇒Total number of people who choose muffin after coffee = \frac{2}{9}x

   Total number of people who choose tart after coffee = \frac{7}{9}x

Also,

Given that

Of those who chose tea,  number of people who chose a muffin : number of people who chose a tart = 5:1

⇒Total number of people who choose muffin after tea = \frac{5}{6}.4x = \frac{20}{6}x

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∴ we get

Total number of people who chooses tart = Total number of people who choose tart after coffee + Total number of people who choose tart after tea

⇒Total number of people who chooses tart = \frac{7}{9}x + \frac{4}{6}x

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                                                                         = \frac{13}{9}x

⇒Total number of people who chooses tart = \frac{13}{9}x

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Fraction of the people chose a tart = \frac{People choose tart}{Total people}

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                                                           = \frac{13}{45}

⇒Fraction of the people chose a tart = \frac{13}{45}

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