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Suppose babies born in a large hospital have a mean weight of 3242 grams, and a standard deviation of 446 grams. If 107 babies a

777dan777 [17]

Answer:

64.76% probability that the mean weight of the sample babies would differ from the population mean by less than 40 grams

Step-by-step explanation:

To solve this question, we have 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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 3242, \sigma = 446, n = 107, s = \frac{446}{\sqrt{107}} = 43.12$

What is the probability that the mean weight of the sample babies would differ from the population mean by less than 40 grams

This is the pvalue of Z when X = 3242 + 40 = 3282 subtracted by the pvalue of Z when 3242 - 40 = 3202

X = 3282

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

By the Central Limit Theorem

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

$Z = \frac{3282 - 3242}{43.12}$

$Z = 0.93$

$Z = 0.93$ has a pvalue of 0.8238.

X = 3202

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

$Z = \frac{3202 - 3242}{43.12}$

$Z = -0.93$

$Z = -0.93$ has a pvalue of 0.1762

0.8238 - 0.1762 = 0.6476

64.76% probability that the mean weight of the sample babies would differ from the population mean by less than 40 grams

5 0

3 years ago

what key feature(s) can be easily identified from standard form? Explain how each key feature is related to the rollercoaster. U

raketka [301]

Answer:

Step-by-step explanation:

Key features

when t = 0

the initial height is 143/3 = 47⅔ ft

initial velocity is -310/3 = -103⅓ ft/s (downward)

initial acceleration is 2(64) = 128 ft/s² (upward)

I would not like to ride this roller coaster!

that's about four times the acceleration of gravity, and it only increases as the car gets to the bottom of the curve at t = 1 s

For part 3

I'm not sure what they mean by "not realistic"

while the initial acceleration is high. the acceleration at t = 1 is zero except that in 'reality' the car would have to be going through a curve to change direction from down to up. That would create very high centripetal acceleration and therefore centripetal forces.

5 0

2 years ago

Two rectangles are similar. The ratio of their corresponding sides is 1:4.

larisa [96]

ratio of perimeter is the same as ratio of sides so perimeter would be 1:4

since area is in square units you need to square the ratio (1:4)^2 which is 1:16

7 0

4 years ago

Marisol rode her bicycle each day for five days. estimate how far she biked in all. round each number to the nearest whole numbe

o-na [289]

Marisol biked a total of 71 miles. On the other hand, she biked about 10 more miles on Wednesday than on Thursday.

<h3>How to round numbers?</h3>

The general rule is to move the decimal number to its nearest tenth. For example, 5.6 should be rounded as 6 but 5.1 should be rounded as 5.

Now, let's round the distance covered by Marisol each day:

Monday: 12.3 = 12
Tuesday: 14.1 = 14
Wednesday: 17.7= 18
Thursday: 11.8 = 12
Friday: 15.2 = 15

<h3>What distance did Marisol covered?</h3>

To know this just add the distance every day:

12 + 14 +18 + 12 + 15 = 71 miles

<h3>How much more did she bike on Wednesday than on Thursday?</h3>

Distance covered on Wednesday - distance covered on Thursday

18 - 12 = 6 miles

Note: This question is incomplete; here is the missing information:

Monday 12.3
Tuesday 14.1
Wednesday 17.7
Thursday 11.8
Friday 15.2

Learn more about addition in: brainly.com/question/17407789

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8 0

1 year ago

A school bus has 25 seats, with 5 rows of 5 seats. 10 students from 2nd grade and 5 students from 1st grade travel on the bus. H

andre [41]

Answer:

(Answer in attachment, explanation below)

Step-by-step explanation:

The answer is B. 5P5 x 20P15.

This is because to make the second grade students to sit in the first row we have 5 seats and 5 students so we will permute the 5 students to those 5 seats. So 5P5.

Now we are left with 20 seats and 15 first grade students so we can simply permute those 15 students into those 20 seats. So 20P15.

Finally using the counting rule principle we will multiply both of these so 5P5 x 20P15.

No. of students from first grade = 15

No. of students from second grade = 5

There are 5 rows of seats

Each row contains 5 seats

Total seats = 25

No. of ways for second-grade students occupy the first row(i.e first 5 seats) =

Remaining seats = 20

No. of students from first grade = 15

So, No. of ways for first-grade students occupy remaining seats =

So, No. of ways for the students can be seated if all of the second-grade students occupy the first row =

So, Option B is true

Hence No. of ways for the students can be seated if all of the second-grade students occupy the first row is

7 0

3 years ago