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spayn [35]
3 years ago
10

1. A population with a normal distribution has a mean of 104 and standard deviation 15. A sample of 30 items is taken from that

population. (a) (4 points) What is the probability of the sample mean being not less than 103?
Mathematics
1 answer:
Pie3 years ago
4 0

Answer:

0.3575

Step-by-step explanation:

A population with a normal distribution has a mean of 104 and a standard deviation of 15. A sample of 30 items is taken from that population. (a) (4 points) What is the probability of the sample mean is not less than 103?

The probability of the sample mean is not less than 103 means the sample mean is equal to 103

We solve using the z score formula

z = (x-μ)/σ/√n

where

x is the raw score = 103

μ is the population mean = 104

σ is the population standard deviation = 15

n is the random number of sample = 30

z = 103 - 104/15/√30

z = -1/2.7386127875

z = -0.36515

Probability value from Z-Table:

P(x≤ 103) = 0.3575

Therefore, the probability of the sample mean is not less than 103 is 0.3575

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1) Put the numbers in order: 40, 45, 50, 60, 60, 75, 90, 90, 120
2) Find the median: Median is 60 (the 2nd one)
3) Place parentheses around the numbers above and below the median. For easy identification of Q1 and Q3. (40, 45, 50, 60,) 60, (75, 90, 90, 120)
4) Find the Q1 and Q3. Q1 = median of the lower half of the data; Q3 = median of the higher half of the data. Q1 and Q3 have even sets so its median cannot be defined.
5) Had both sets contain odd sets, the median of Q1 is subtracted from the median of Q3 to get the IQR.

We can then use the Alternative definition of IQR.
IQR is the difference between the largest and smallest values in the middle 50% of a set data.

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Middle 50% is 50, 60, 60, 75, 90; IQR = Largest value - smallest value;

IQR = 90 - 50 = 40



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Step-by-step explanation:

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For a better understanding of the solution provided here please find the diagram attached.

Please note that in coordinate geometry, the coordinates of the midpoint of a line segment is always the average of the coordinates of the endpoints of that line segment.

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Thus for our question the endpoints are (x_E, y_E) and (x_F, y_F) and hence the midpoint will be:

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