What is the answer to this equation

Terri Vogel, an amateur motorcycle racer, averages 129.71 seconds per 2.5 mile lap (in a 7 lap race) with a standard deviation o

Vikki [24]

Answer:

(a) The percent of her laps that are completed in less than 130 seconds is 55%.

(b) The fastest 3% of her laps are under 125.42 seconds.

(c) The middle 80% of her laps are from 126.80 seconds to 132.63 seconds.

Step-by-step explanation:

The random variable X is defined as the number of seconds for a randomly selected lap.

The random variable X is normally distributed with mean, μ = 129.71 seconds and standard deviation, σ = 2.28 seconds.

Thus, $X\sim N(129.71,\ 2.28^{2})$ .

(a)

Compute the probability that a lap is completes in less than 130 seconds as follows:

$P(X$

$=P(Z$

The percentage is, 0.55 × 100 = 55%.

Thus, the percent of her laps that are completed in less than 130 seconds is 55%.

(b)

Let x represents the 3rd percentile.

That is, P (X < x) = 0.03.

⇒ P (Z < z) = 0.03

The value of z for the above probability is:

z = -1.88

Compute the value of x as follows:

$z=\frac{x-\mu}{\sigma}\\-1.88=\frac{x-129.71}{2.28}\\x=129.71-(1.88\times 2.28)\\x=125.4236\\x\approx 125.42$

Thus, the fastest 3% of her laps are under 125.42 seconds.

(c)

Let x₁ and x₂ be the values between which the middle 80% of the distribution lie.

That is,

$P(x_{1}$

The value of z for the above probability is:

z = 1.28

Compute the values of x₁ and x₂ as follows:

$-z=\frac{x_{1}-\mu}{\sigma}\\-1.28=\frac{x_{1}-129.71}{2.28}\\x_{1}=129.71-(1.28\times 2.28)\\x=126.7916\\x\approx 126.80$ $z=\frac{x_{2}-\mu}{\sigma}\\1.28=\frac{x_{2}-129.71}{2.28}\\x_{2}=129.71+(1.28\times 2.28)\\x=132.6284\\x\approx 132.63$

Thus, the middle 80% of her laps are from 126.80 seconds to 132.63 seconds.

5 0

3 years ago

PLEASEE HELPP....Simplify the expression using properties of exponents.

Aleks04 [339]

Answer:

D

Step-by-step explanation:

Using the rule of exponents

$\frac{a^{n} }{a^{m} }$ = $\frac{1}{a^{(m-n)} }$

Given

$\frac{25a^{-5}b^{-8} }{5a^{4}b }$

= $\frac{25}{5}$ × $\frac{a^{-5} }{a^{4} }$ × $\frac{b^{-8} }{b^{1} }$

= 5 × $\frac{1}{a^{(4-(-5))} }$ × $\frac{1}{b^{(1-(-8))} }$

= 5 × $\frac{1}{a^{9} }$ × $\frac{1}{b^{9} }$

= $\frac{5}{a^{9}b^{9} }$ → D

5 0

2 years ago

Use elimination to solve 4x – 2y = -14 3x - y = -8

Xelga [282]

X = -1, y = 5. Hope this helps

8 0

2 years ago

I really need this answer as soon as possible please anyone

Contact [7]

The answer is 55!!!!

5 0

3 years ago

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Can someone help i put a random answer

Gre4nikov [31]

P= 36 units............,

4 0

3 years ago

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What is the answer to this equation - 2w+21=-8w+36