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4 years ago

W is a normally distributed random variable with mean 22 and variance 25. The probability that W is less than 9.7 equals:

Mathematics

1 answer:

Musya8 [376]4 years ago

8 0

Answer:

0.006946

Step-by-step explanation:

Given that :

W = normally distributed random variable

Mean(m) = 22

Variance = 25 ; standard deviation =√variance ;

Standard deviation (σ) = √25 = 5

Probability that W < 9.7

x = 9.7

Zscore = (x - m) / σ

Zscore = (9.7 - 22) / 5

Zscore = - 12.3 / 5

Zscore = - 2.46

P(Z < - 2.46) = 0.006946

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Answer:

The height at time of 12.1 seconds is approximately 729.2562 feet

Step-by-step explanation:

The general form of the quadratic regression equation is y = A + Bx + Cx²

The quadratic regression formula is given as follows;

$B = \dfrac{S_{xy}S_{x'x'}-S_{x'y}S_{xx'}}{S_{xx}S_{x'x'} -(S_{xx'})^2}$

$C = \dfrac{S_{x'y}S_{xx}-S_{xy}S_{xx'}}{S_{xx}S_{x'x'} -(S_{xx'})^2}$

$A = \bar y - B \bar x - C \bar {x^2}$

$S_{xx} = \Sigma (x_i - \bar x)^2$

$S_{xy} = \Sigma (x_i - \bar x)(y_i - \bar y)$

$S_{xx'} = \Sigma (x_i - \bar x)(x^2_i - \bar {x^2})$

$S_{x'x'} = \Sigma (x^2_i - \bar {x^2})^2$

$S_{x'y} = \Sigma (x^2_i - \bar {x^2})(y_i - \bar {y})$

Solving using an online quadratic regression calculator, gives;

A = 2.5643259

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Substituting gives;

y = 2.5643259 + 246.6374865·x -15.41986006·x²

When time, x = 12.1, we have;

y = 2.5643259 + 246.6374865×12.1 -15.41986006×12.1²≈ 729.2562 feet

The height at time of 12.1 seconds ≈ 729.2562 feet.

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