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bixtya [17]
2 years ago
10

Suppose you can somehow choose two people at random who took the SAT in 2014. A reminder that scores were Normally distributed w

ith mean and stanard deviation of 1497 and 322, respectively. What is the probability that both of them scored above a 1520? Assume that the scores of the two test takers are independent.
Mathematics
1 answer:
Sindrei [870]2 years ago
8 0

Answer:

22.29% probability that both of them scored above a 1520

Step-by-step explanation:

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

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

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

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:

\mu = 1497, \sigma = 322

The first step to solve the question is find the probability that a student has of scoring above 1520, which is 1 subtracted by the pvalue of Z when X = 1520.

So

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

Z = \frac{1520 - 1497}{322}

Z = 0.07

Z = 0.07 has a pvalue of 0.5279

1 - 0.5279 = 0.4721

Each students has a 0.4721 probability of scoring above 1520.

What is the probability that both of them scored above a 1520?

Each students has a 0.4721 probability of scoring above 1520. So

P = 0.4721*0.4721 = 0.2229

22.29% probability that both of them scored above a 1520

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Answer:

Step-by-step explanation:

9(2.3n+6)+10.45>43.7

(9*2.3n)+(9*6)+10.45>43.7

20.7n+54+10.45>43.7

20.7n+64.45>43.7

7 0
3 years ago
A shopkeeper allows 10% discount on the marked price of a bicycle. If a costomer pays Rs 4068 with 13% VAT find the marked price
Over [174]

\large{ \tt{❁ \: S \: O \: L \: U \: T \: I \: O \: N \: ❁}}

  • We're provided - Discount % = 10 % , Cost with VAT [ SP with VAT ] = Rs 4068 & VAT % = 13%. We're asked to find out the marked price of the bicycle. Let's start :

\large{ \tt{❇ \: FIND \: SP \: WITHOUT \: VAT \: / \: SP\: ❇}}

\large{ \tt{❃ \: SP  \: with \: VAT= SP + VAT\% \: of \: SP}}

\large{ \tt{⇢ \: 4068 = SP + 13\% \: of \: SP}}

\large{ \tt{⇢ \: 4068 = SP +  \frac{13}{100}  \: sp}}

\large{ \tt{⇢ \: 4068 =  \frac{100 \:  \: SP + 13 \: SP}{100} }}

\large{ \tt{⇢ \: 4068 =  \frac{113 \: SP}{100} }}

\large{ \tt{⇢ \: 113 \: SP = 406800}}

\large{ \tt{⇢ \: SP =  \frac{406800}{113} }}

\large{ \tt{⇢ \: SP = 3600}}

  • Hence , SP = Rs 3600

\large{ \tt{✽ \: NOW , \: FIND \: THE \: MP \:✽ }}

  • Let Marked Price [ MP ] be x.

\large {\tt{❃ \: SP = MP - dis\% \: of \: MP}}

\large{ \tt{⇾ \: 3600 = x - 10\% \: of \: x}}

\large{ \tt{⇾ \: 3600 = x -  \frac{10}{100} } \: x}

\large{ \tt{⇾ \: 3600 =  \frac{100x - 10x}{100} }}

\large{ \tt{⇾ \: 3600 =  \frac{90x}{100} }}

\large{ \tt{⇾ \: 90x = 360000}}

\large{ \tt{⇾ \: x =  \frac{360000}{90} }}

\large{ \tt{⇾ \: x = Rs \: 4000}}

\large{ \boxed{ \boxed{ \tt{☂ \: OUR \: FINAL \: ANSWER :  \boxed {\tt {\: Rs \: 4000}}}}}}

  • Hope I helped! Let me know if you have any questions regarding my answer and don't hesitate to reach out to me if you need any assistance! :)
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2 years ago
Surveyors wished to know the distance across a lake between A and B. They measured the distance from B to C as 100 m and the ang
kherson [118]

Answer:

<h3>AB ≈ 70m</h3>

Step-by-step explanation:

Check the attachment for the diagram.

You can see from the diagram that it is a right angled triangle with opposite side AB and adjacent side BC. Using SOH, CAH, TOA trig identity to get the length of AB. According to TOA;

tan 35° = opposite/adjacent

tan 35° = AB/BC

tan 35° = AB/100

AB = 100tan35°

AB = 100 * 0.7002

AB = 70.02m

Hence the distance across a lake between A and B is approximately 70m

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$109 X 20%
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