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pishuonlain [190]
3 years ago
9

A ramp extends from the back of a truck bed to the ground. The back of the truck bed is 3 ft above the ground. The horizontal di

stance from the spot below the back of the truck bed to the bottom of the ramp is 8 ft.
How long is the ramp?
Mathematics
1 answer:
NemiM [27]3 years ago
3 0
Use pythagoras' theorem. So,
3^2 + 8^2 = 9 + 64 = 73
So the ramp is equal to the square root of 73.
Hope this helps!
- Timo

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Here it is,
20mm/m = 1200 mm/h
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2 years ago
Suppose a simple random sample of size n= 11 is obtained from a population with u = 62 and a = 14.
Eduardwww [97]

Answer:

a) C. The population must be normally distributed.

b) P(x < 65.8) = 0.8159

c) P(x > 64.2) = 0.3015

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use 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 normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

\mu = 62, \sigma = 14, n = 11, s = \frac{14}{\sqrt{11}} = 4.22

(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample me

n < 30, so the distribution of the population must be normal.

The correct answer is:

C. The population must be normally distributed.

(b) Assuming the normal model can be used, determine P(x < 65.8).

This is the pvalue of Z when X = 65.8. So

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

By the Central Limit Theorem

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

Z = \frac{65.8 - 62}{4.22}

Z = 0.9

Z = 0.9 has a pvalue of 0.8159.

So

P(x < 65.8) = 0.8159

(c) Assuming the normal model can be used, determine P(x > 64.2).

This is 1 subtracted by the pvalue of Z when X = 64.2. So

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

Z = \frac{64.2 - 62}{4.22}

Z = 0.52

Z = 0.52 has a pvalue of 0.6985.

1 - 0.6985 = 0.3015

So

P(x > 64.2) = 0.3015

7 0
3 years ago
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