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SVEN [57.7K]
3 years ago
8

A set of computer science exam scores are normally distributed with a mean of 71.33 point, and a standard deviation of 3 points.

What proportion of the exam scores are between 68 and 77.99 points?
Mathematics
1 answer:
Bess [88]3 years ago
5 0

Answer: 0.86 of the exam scores are between 68 and 77.99 points

Step-by-step explanation:

Since the set of computer science exam scores are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = computer science exam scores .

µ = mean score

σ = standard deviation

From the information given,

µ = 71.33 points

σ = 3 points

We want to find the proportion of the exam scores are between 68 and 77.99 points. It is expressed as

P(68 ≤ x ≤ 77.99)

For x = 68,

z = (68 - 71.33)/3 = - 1.11

Looking at the normal distribution table, the probability corresponding to the z score is 0.13

For x = 68,

z = (77.99 - 71.33)/3 = 2.22

Looking at the normal distribution table, the probability corresponding to the z score is 0.99

P(68 ≤ x ≤ 77.99) = 0.99 - 0.13 = 0.86

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Answer:

Deepak: 4 t-shirts,

Tarun: 12 t-shirts,

Mahesh: 14 t-shirts.

Step-by-step explanation:

Let x represent number of t-shirts that Deepak has.

Please consider the complete question.

Tarun has 4 t-shirt more than twice the number of T-shirts Deepak has. Mahesh has 2 more than thrice the number of T-shirts Deepak has. If the ratio of the t-shirt that Tarun and Mahesh have is 6 : 7, find out the number of the t-shirt each of them has.​

Since Tarun has 4 t-shirt more than twice the number of T-shirts Deepak has, so the number of t-shirts that Tarun has would be 2x+4.

We are also told that Mahesh has 2 more than thrice the number of T-shirts Deepak has. So the number of t-shirts that Mahesh has would be 3x+2.

Since the ratio of the t-shirt that Tarun and Mahesh have is 6 : 7, so we can represent this information in an equation as:

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Cross multiply:

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18x-14x+12-12=14x-14x+28-12

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Therefore, Deepak has 4 t-shirts.

The number of t-shirts that Tarun has would be 2x+4\Rightarrow 2(4)+4=4+4=12

Therefore, Tarun has 12 t-shirts.

The number of t-shirts that Mahesh has would be 3x+2\Rightarrow 3(4)+2=12+2=14

Therefore, Mahesh has 14 t-shirts.

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