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djverab [1.8K]
2 years ago
7

Need answer with step I will give ve you 35 points.After 12 years Kishor will be 3 times as old as he was 4 years ago . Find the

present age .
Mathematics
1 answer:
tatyana61 [14]2 years ago
8 0

Answer:

<u>12 years</u>

Step-by-step explanation:

Let Kishor's present age be denoted by x.

According to the question :

  • He will 3 times as old as he was 4 years ago after 12 years

Therefore, the equation is :

  • x + 12 = 3(x - 4)

Solving :

  • x + 12 = 3x - 12
  • 3x - x = 12 + 12
  • 2x = 24
  • x = <u>12 years</u>

<u></u>

Hence, Kishor's present age is <u>12 years</u>.

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b) 81.64% probability that the sample mean will be between 5.9 and 6.7 hours.

Step-by-step explanation:

To solve this question, it is important to know the Normal probability distribution and the Central Limit Theorem

Normal probability distribution

Problems of normally distributed samples can be 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation \frac{\sigma}{\sqrt{n}}.

In this problem, we have that:

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This is the pvalue of Z when X = 7.1 subtracted by the pvalue of Z when X = 5.5.

By the Central Limit Theorem, the formula for Z is:

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X = 5.5

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So there is a 0.9962 - 0.0038 = 0.9924 = 99.24% chance HLI will find a sample mean between 5.5 and 7.1 hours.

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Z = -1.33

Z = -1.33 has a pvalue of 0.0918.

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