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tiny-mole [99]
3 years ago
9

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate

the mean score μμ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 6.4. Suppose that (unknown to you) the mean score of those taking the MCAT on your campus is 24.
In answering the following, use z-scores rounded to two decimal places.

If you choose one student at random, what is the probability (±±0.0001) that the student's score is between 20 and 30?

You sample 22 students. What is the standard deviation (±±0.01) of sampling distribution of their average score x¯¯¯x¯?

What is the probability (±±0.0001) that the mean score of your sample is between 20 and 30?
Mathematics
1 answer:
yKpoI14uk [10]3 years ago
5 0

Answer:

a) 0.5588

b) 0.9984

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 24

Standard Deviation, σ = 6.4

We are given that the distribution of score is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}        

a) P(score between 20 and 30)

P(20 \leq x \leq 30) = P(\displaystyle\frac{20 - 24}{6.4} \leq z \leq \displaystyle\frac{30-24}{6.4}) = P(-0.62 \leq z \leq 0.94)\\\\= P(z \leq 0.94) - P(z < -0.62)\\= 0.8264 - 0.2676 = 0.5588 = 55.88\%

P(20 \leq x \leq 30) = 55.88\%

b) Sampling distribution

Sample size, n = 22

The sample will follow a normal distribution with mean 24 and standard deviation,

s = \dfrac{\sigma}{\sqrt{n}} = \dfrac{6.4}{\sqrt{22}} =1.36

c) P(mean score of sample is between 20 and 30)

P(20 \leq x \leq 30) = P(\displaystyle\frac{20 - 24}{1.36} \leq z \leq \displaystyle\frac{30-24}{1.36}) = P(-2.94 \leq z \leq 4.41)\\\\= P(z \leq 4.41) - P(z < -2.94)\\= 1 - 0.0016 = 0.9984 = 99.84\%

P(20 \leq x \leq 30) =99.84\%

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I REALLY NEED HELP ON THIS PLS HELP
Eva8 [605]

Part (a)

Answer: See the attached image below to see the filled out chart.

Note how rational and irrational numbers have nothing in common. This means there is no overlap. So they go in the rectangles. The two sets of numbers join up to form the entire set of real numbers.

Integers are in the set of rational numbers. This is because something like 7 is also 7/1; however 1/7 is not an integer. So not all rational numbers are integers. The larger purple circle is the set of integers.

The smaller blue circle is the set of whole numbers. The set of whole numbers is a subset of integers. Recall the set of whole numbers is {0,1,2,3,...} so we ignore the negative values only focusing on 0 and positive numbers that don't have any fractional values. In contrast, the set of integers is {..., -3, -2, -1, 0, 1, 2, 3, ...} here we do include the negatives.

============================================================

Part (b)

1) Some irrational numbers are integers.

This is false. An irrational number is not rational. The set of integers is contained entirely in the set of rational numbers.

---------------------------------

2) Some whole numbers are not irrational numbers.

This is false. The statement implies that some whole numbers are irrational, but the set of whole numbers is inside the set of rational numbers, which has no overlap with the irrationals. The statement should be "All whole numbers are not irrational numbers".

---------------------------------

3) All rational numbers are whole numbers.

This is false. A rational number like 1/3 is not a whole number.

---------------------------------

4) All integers are whole numbers

This is false. An integer like -44 is not a whole number because the set of whole numbers is {0,1,2,3,...} and we're not including negative values.

---------------------------------

In summary, all four statements for part (b) are false.

8 0
2 years ago
Read 2 more answers
A line through the origin has a slope of 1 / 3. Carlos thinks the slope of a perpendicular line at the origin will be 3.
OLEGan [10]

Answer:

Carlos is incorrect.

Step-by-step explanation:

We have been given that a line through the origin has a slope of \frac{1}{3}. Carlos thinks the slope of a perpendicular line at the origin will be 3.

We know that the slope of a perpendicular line to a given line is always negative reciprocal of the slope of the given line.

The slope of the perpendicular line at the origin will be negative reciprocal of \frac{1}{3}.

Let us find negative reciprocal of \frac{1}{3} as:

-\frac{1}{\frac{1}{3}}=-\frac{1\cdot 3}{1}=-3

Since the slope of a perpendicular line at the origin is -3, therefore, Carlos is incorrect.

4 0
3 years ago
I am between 24 and 34 u say my name when u count by twos from 0 u say my name when u count by 5 from 0 what number am i
katen-ka-za [31]
Hi there 
let me help you out 

The answer is 30 
To find the answer you have to find the multiples of 2 and 5 
2,4,6,8,10,12, 14,16,18,20,22,24,26,28,30,32,34,
5,10,15,20,25,30

30 comes in both time tables. 
it also does not cross 34

hope this helps you 

4 0
3 years ago
Jonas weight 63 pounds. jane weight 67 pounds. round each number to the nearest ten.
IrinaVladis [17]

Answer:

Jonas = 60 pounds

Jane = 70 pounds

Remember- 5 or more, raise the score. 4 or less, let it rest.

Jonas is 63 pounds. 3 is less than 4, so rounded to the nearest ten would be 60 pounds.

Meanwhile, Jane is 67 pounds. 7 is more than 5, so we will raise the score.

So, 67 rounded to the nearest ten would be 70.

You have your answers. 60 and 70. Hope this helps!

4 0
3 years ago
Read 2 more answers
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hjlf

Answer:

263.25 cm

Step-by-step explanation:

5 0
3 years ago
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