How many twenties have the same value as £9.00

The overhead reach distances of adult females are normally distributed with a mean of 197.5 cm197.5 cm and a standard deviation

fiasKO [112]

Answer:

a) 5.37% probability that an individual distance is greater than 210.9 cm

b) 75.80% probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

c) Because the underlying distribution is normal. We only have to verify the sample size if the underlying population is not normal.

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 question, we have that:

$\mu = 197.5, \sigma = 8.3$

a. Find the probability that an individual distance is greater than 210.9 cm

This is 1 subtracted by the pvalue of Z when X = 210.9. So

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

$Z = \frac{210.9 - 197.5}{8.3}$

$Z = 1.61$

$Z = 1.61$ has a pvalue of 0.9463.

1 - 0.9463 = 0.0537

5.37% probability that an individual distance is greater than 210.9 cm.

b. Find the probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

Now $n = 15, s = \frac{8.3}{\sqrt{15}} = 2.14$

This probability is 1 subtracted by the pvalue of Z when X = 196. Then

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

By the Central Limit Theorem

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

$Z = \frac{196 - 197.5}{2.14}$

$Z = -0.7$

$Z = -0.7$ has a pvalue of 0.2420.

1 - 0.2420 = 0.7580

75.80% probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

The underlying distribution(overhead reach distances of adult females) is normal, which means that the sample size requirement(being at least 30) does not apply.

5 0

3 years ago

Simplify the expressions plz help

Sophie [7]

Alright, so the answer for:

3) is 3v + 4

6 0

3 years ago

Please help ASAP! i will mark brainliest

Kitty [74]

Use two pints on the graph to find the slope:

(0,0) and (5,1)

Slope = Change in Y over the change in x.

Slope = (1-0) / (5-0) = 1/5 = 0.20

The slope of the given equation is 0.25 which is greater than 0.20.

The unit rate is greater in the equation.

8 0

3 years ago

HELP ME PLZ answer question below

Ronch [10]

Answer:

11. -2

12. +0.5

Step-by-step explanation:

11. as x increases by 1, y decreases by 2, -2/1 = -2 the ROC is -2 (rate of change)

12. as x increases by 2, y increases by 1, 1/2 = 0.5, ROC is +0.5

8 0

3 years ago

Read 2 more answers

When finding the sum of 512 and –614, Josh used a left-to-right algorithm to compute the answer. He first added the hundred’s di

Georgia [21]

Answer:

Yes, Josh's answer is correct as  –102 is the correct answer.

Josh have computed the sum as:

If the two integers having different signs, we need to subtract the absolute values (the digits without signs) and then just make sure to keep the sign of the number with the larger absolute value.

− 6 1 4

+ + 5 1 2

_________

- 1 0 2

_________

Staring from right, − 614 + (+512) = -102 can be obtained by first adding 2 in negative 4, then adding 1 in negative 1, and lastly adding 5 in negative 6.

Ultimately we can say that Negative 614 plus Positive 514 equals Negative 102.

So, the sum of 512 and –614 is -102 i.e − 614 + (+512) = -102

Step-by-step explanation:

This is how Josh used a left-to-right algorithm to compute the answer:

Adding the hundred’s digits 500 + (–600) = –100
Adding the ten's digits 10 + (–10) = 0
Lastly, adding 2 + (–4) = –2
End result –100 + 0 + (–2) = –102

Yes, Josh's answer is correct. 

How else could Josh have computed the sum?

Before mentioning how Josh could have computed the sum. Here are some of the facts about sum of numbers:

The sum of two negative integers is a negative integer. For example,

Adding two negative integers: -3 and -5

-3 + -5 = -8

Please, you don't need to confuse the sign or symbol of the integer with the operation being performed.

Just note -3 + -5 = -8 which is read as is read as Negative 3 plus negative 5 equals negative 8.

The sum of two positive integers is a positive integer.

Adding two positive integers: ⁺3 and ⁺5

(⁺3) + (⁺5) = ⁺8

Please, you don't need to confuse the sign or symbol of the integer with the operation being performed.

Just note ⁺3 + ⁺5 = ⁺8 which is read as is read as Positive 3 plus positive 5 equals positive 8.

To add a positive and a negative integer

As +(+) are like signs, so they become a positive sign. Such as:

−5 + (+ 1) = −5 + 1 = -4

As

+ + ⇒ +

+ − ⇒ −

− + ⇒ −

− − ⇒ +

If the two integers having different signs, we need to subtract the absolute values (the digits without signs) and then just make sure to keep the sign of the number with the larger absolute value.

So, What is −614 + (+512)?

− 6 1 4

+ + 5 1 2

_________

- 1 0 2

_________

Staring from right, − 614 + (+512) = -102 can be obtained by first adding 2 in negative 4, then adding 1 in negative 1, and lastly adding 5 in negative 6.

Ultimately we can say that Negative 614 plus Positive 514 equals Negative 102.

So, the sum of 512 and –614 is -102 i.e − 614 + (+512) = -102

Keywords: integer, sum, numbers, digit

Learn more about sum of integers from brainly.com/question/591533

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3 0

3 years ago