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ivann1987 [24]
2 years ago
12

The Office of Student Services at a large western state university maintains information on the study habits of its full-time st

udents. Their studies indicate that the mean amount of time undergraduate students study per week is 20 hours. The hours studied follows the normal distribution with a population standard deviation of seven hours. Suppose we select a random sample of 125 current students. What is the probability that the mean of this sample is between 19.25 hours and 21.0 hours
Mathematics
1 answer:
ExtremeBDS [4]2 years ago
8 0

There is a probability of 77% that the mean of this sample is between 19.25 hours and 21.0 hours

Z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

z=\frac{x-\mu}{\sigma/\sqrt{n} } \\\\where\ x=raw\ score,\mu=mean,\sigma=standard\ deviation,n=sample\ size

Given that μ = 20, σ = 7, n = 125.

For x = 19.25:

z=\frac{19.25-20}{7/\sqrt{125} } =-1.20\\\\\\For\ x=21:\\\\z=\frac{21-20}{7/\sqrt{125} } =0.62

From the normal distribution table, P(-1.20 < z < 0.62) = P(z < 0.62) - P(z < -1.2) = 0.8849 - 0.1151 = 0.7698 = 77%

There is a probability of 77% that the mean of this sample is between 19.25 hours and 21.0 hours

Find out more on z score at: brainly.com/question/25638875

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Answer:

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Step-by-step explanation:

Volume of a cone(V) is given by:

V = \frac{1}{3} \pi r^2h             ....[1]

where,

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As per the statement:

A cone with radius 5 units and ts volume is 105 cubic units

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Substitute these given values and use \pi = 3.14 in [1] we have;

105 = \frac{1}{3} \cdot 3.14 \cdot 5^2 \cdot h

Multiply both sides by 3 we have;

⇒315 = 78.5 \cdot h

Divide both sides by 78.5 we have;

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or

h = 4.01273885 units

Therefore, the height of the cone is, 4.01273885 units

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36inch - 2 feet

72inch - 4 feet

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