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shutvik [7]
2 years ago
7

For a normal distribution with mean 47 and standard deviation 6, find the probability of obtaining a value less than 45 or great

er than 49.
Mathematics
1 answer:
Llana [10]2 years ago
4 0

Answer:

0.7392 = 73.92% probability of obtaining a value less than 45 or greater than 49.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean 47 and standard deviation 6

This means that \mu = 47, \sigma = 6

Less than 45:

p-value of Z when X = 45, so:

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

Z = \frac{45 - 47}{6}

Z = -0.3333

Z = -0.3333 has a p-value of 0.3696.

More than 49:

1 subtracted by the p-value of Z when X = 49. So

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

Z = \frac{49 - 47}{6}

Z = 0.3333

Z = 0.3333 has a p-value of 0.6304.

1 - 0.6304 = 0.3996

Less than 45 or greater than 49:

2*0.3696 = 0.7392

0.7392 = 73.92% probability of obtaining a value less than 45 or greater than 49.

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PLS HELP SHOW ALL YOUR WORKING OUT BRAINLIEST! WILL BE GIVEN :D
aliina [53]

Answer:

(a) Five

(b) Thirteenth

Step-by-step explanation:

We have the mean is 12.6 and

that 11 occurs 4 times, 12 occurs 7 times, 13 occurs 9 times, and 14 occurs f times.

How many children are there in all (that is the sum of the frequencies).

4+7+9+f

20+f

Alright so the mean could be found by doing:

\frac{4(11)+7(12)+9(13)+f(14)}{20+f}

But we are given this is also equal to: 12.6.

So we have

\frac{4(11)+7(12)+9(13)+f(14)}{20+f}=12.6

I'm going to simplify what I can on top.

\frac{245+14f}{20+f}=12.6

I'm going to write 12.6 as \frac{12.6}{1} because I want to cross multiply:

\frac{245+14f}{20+f}=\frac{12.6}{1}

(245+14f)(1)=12.6(20+f)

Distribute:

245+14f=252+12.6f

Subtract 12.6f on both sides:

245+1.4f=252

Subtract 245 on both sides:

1.4f=7

Divide both sides by 1.4:

f=5

There are five 14 years old.

(b) I would say 13 is good age to represent this bunch.

The means was 12.6 which when rounded is 13.

The mode is 13 because it is the most occurring

The median is also 13. Why? If you list out the data 13 will be the middle number. Or you could say there are 25 kids and if I divide it by 2, I get 12.5.  This means you only need to count to the 13th kid with the ages in order to tell with the median is.

There are 4 eleven yr olds.

There are 7 twelve yr olds.  That is 11 kids so far.

So the median has to be included in the 9 thirteenth yr olds.

3 0
3 years ago
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