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tatuchka [14]
3 years ago
9

On a random Friday in the fall, 95% of students were present at school. If there are a total of 420 students enrolled, then how

many students were present that day​
Mathematics
1 answer:
-Dominant- [34]3 years ago
4 0

Answer:

399 but I'm not 100 percent sure

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The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 3639 3639 miles, with a var
Andrei [34K]

Answer:

96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles

Step-by-step explanation:

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

A reminder is that the standard deviation is the square root of the variance.

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 \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

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

In this question:

\mu = 3639, \sigma = \sqrt{145161} = 381, n = 41, s = \frac{381}{\sqrt{41}} = 59.5

Probability that the mean of the sample would differ from the population mean by less than 126 miles

This is the pvalue of Z when X = 3639 + 126 = 3765 subtracted by the pvalue of Z when X = 3639 - 126 = 3513. So

X = 3765

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

By the Central Limit Theorem

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

Z = \frac{3765 - 3639}{59.5}

Z = 2.12

Z = 2.12 has a pvalue of 0.983

X = 3513

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

Z = \frac{3513 - 3639}{59.5}

Z = -2.12

Z = -2.12 has a pvalue of 0.017

0.983 - 0.017 = 0.966

96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles

3 0
3 years ago
The probability of choosing a green ball out of a box of balls is 2/9. What are the odds in favor of choosing a green ball?
kirill [66]
The answer is B. 2:7
5 0
3 years ago
Least to greatest<br> 3/4,5/8,3/7,1/3,2/5
tangare [24]

Answer:

1/3 < 2/5 < 3/7 < 5/8 < 3/4

Step-by-step explanation:

Using the given inputs:  

3/4 5/8 3/7 1/3 2/5

The least common denominator (LCD) is: 840.

Rewriting as equivalent fractions with the LCD:

3/4= 630/840

5/8= 525/840

3/7= 360/840

1/3= 280/840

2/5=  336/840  

Sorting this by the numerators of the equivalent fractions in order from least to greatest:

1/3= 280/840=       < 2/5=  336/840=    <     3/7= 360/840=      <    5/8= 525/840=       <     3/4 = 630/840

Therefore, the sorted inputs in order from least to greatest is:

1/3 < 2/5 < 3/7 < 5/8 < 3/4

Hopes this helps!

Have a good evening! :)

5 0
3 years ago
The perimeter of an isosceles triangle is 71 centimeters. The measure of one of the sides is 22 centimeters. What are all the po
denis23 [38]
An isosceles triangle has two equal side lengths and the other side length is different. Therefore, possible measures of the other two sides are either 
22 cm and 27 cm,  or  22 cm and 24.5 cm. 
4 0
3 years ago
Question 3 (10 points)
arlik [135]

Answer:

7.96 × 10⁸ kg

Step-by-step explanation:

Step 1: Given data

  • Mass of the Eiffel Tower (mE): 9.16 × 10⁶ kg
  • Mass of the Golden Gate Bridge (mG): 8.05 × 10⁸ kg

Step 2: Determine how many more kilograms is the mass of the Golden Gate Bridge than the mass of the Eiffel Tower

To determine this ratio, we need to do the following subtraction.

mG - mE = 8.05 × 10⁸ kg - 9.16 × 10⁶ kg = 7.96 × 10⁸ kg

The Golden Gate Bridge has approximately 7.96 × 10⁸ kg more than the Eiffel Tower.

6 0
2 years ago
Read 2 more answers
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