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boyakko [2]
3 years ago
9

A culture of bacteria has an initial population of 7100 bacteria and doubles every 2

Mathematics
1 answer:
Allisa [31]3 years ago
3 0

Answer:

Pt=1285237.2855≈ 1285237

YOUR WELCOME :)

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The composite scores of individual students on the ACT college entrance examination in 2009 followed a normal distribution with
Mumz [18]

Answer:

35.57% probability that a single student randomly chosen from all those taking the test scores 23 or higher.

0.41% probability that a simple random sample of 50 students chosen from all those taking the test has an average score of 23 or higher.

The lower the standard deviation, the higher the z-score, which means that the higher the pvalue of X = 23, which means there is a lower probability of scoring above 23. By the Central Limit Theorem, as the sample size increases, the standard deviation decreases, which means that Z increases.

Step-by-step explanation:

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

Normal probability distribution

Problems of normally distributed samples are 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 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 problem, we have that:

\mu = 21.1, \sigma = 5.1

What is the probability that a single student randomly chosen from all those taking the test scores 23 or higher?

This is the pvalue of Z when X = 23.

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

Z = \frac{23 - 21.1}{5.1}

Z = 0.37

Z = 0.37 has a pvalue of 0.6443

1 - 0.6443 = 0.3557

35.57% probability that a single student randomly chosen from all those taking the test scores 23 or higher.

What is the probability that a simple random sample of 50 students chosen from all those taking the test has an average score of 23 or higher?

Now we use the central limit theorem, so n = 50, s = \frac{5.1}{\sqrt{50}} = 0.72

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

Z = \frac{23 - 21.1}{0.72}

Z = 2.64

Z = 2.64 has a pvalue of 0.9959

1 - 0.9959 = 0.0041

0.41% probability that a simple random sample of 50 students chosen from all those taking the test has an average score of 23 or higher.

Why is it more likely that a single student would score this high instead of the sample of students?

The lower the standard deviation, the higher the z-score, which means that the higher the pvalue of X = 23, which means there is a lower probability of scoring above 23. By the Central Limit Theorem, as the sample size increases, the standard deviation decreases, which means that Z increases.

5 0
3 years ago
What is the distance between (0, 0) and (-7, -3)? Round your answer to the nearest tenth.
lyudmila [28]

Answer:

Distance = -7.6

Step-by-step explanation:

Using Distance Formula, √((x2-x1)^2 + (y2-y1)^2)

√((-7 - 0))^2 + (-3 - 0)^2) = 7.6

7 0
2 years ago
i need help with b. How would the ordered pairs be different if the outdoor temperature were recorded every hour for 4 consecuti
marishachu [46]

Answer:

Just match values.

At 1 hour you have 60 degrees

At 2 hour 65

At 3 70 degrees

At 4 75 degrees

As You can see the temperature varies by 5 degrees

8 0
3 years ago
Are the triangles congruent?<br><br>a-yes<br>b-no<br>c-not enough information<br>​
ioda

the right answer is yes

5 0
3 years ago
Jenna lives 4 3/10 miles from school. She estimates that she travels 4×2×5 or 40 miles each week. Is her estimate an overestimat
patriot [66]
It will be an underestimate the answer is 43 I hoped that helped?
5 0
3 years ago
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