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Alexxandr
4 months ago
10

The heights of 1000 students are approximately normally distributed with a mean of 174.5 centimeters and a standard deviation of

6.9 centimeters. suppose 200 random samples of size 25 are drawn from this population and the means recorded to the nearest tenth of a centimeter. determine (a) the mean and standard deviation of the sampling distribution of x¯; (b) the number of sample means that falls between 172.5 and 175.8 centimeters inclusive; (c) the number of sample means falling below 172.0 centimeters.
Mathematics
1 answer:
PIT_PIT [12.4K]4 months ago
8 0
A. Mean and standard deviation.

The sampling distribution’s mean closely matches the population mean. Since the population mean is 174.5, the sampling distribution’s mean equals this value.

The standard deviation of the sampling distribution is:

            σₓ̄ = σ / √n

Plugging in values:

            σₓ̄ = 6.9 / √25 = 1.38

b. Calculate z-scores for both values:
         
      z = (value - mean) / standard deviation

For 172.5:
     z = (172.5 - 174.5) / 1.38 = -1.49
Corresponding probability ≈ 0.068

For 175.8:
   z = (175.8 - 174.5) / 1.38 = 0.94
Corresponding probability ≈ 0.83

The difference between these probabilities is 0.762.

Approximately 0.762 × 200 = 152 sample means lie between 172.5 and 175.8.

c. Z-score for 172 cm:

    z = (172 - 174.5) / 1.38 = -1.81
Probability ≈ 0.03

Hence, samples with means below 172 cm equal 0.03 × 200 = 6.
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Step-by-step explanation:

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3 months ago
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Answer:


Step-by-step explanation:




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3 months ago
A rectangle has area 25 m2. express the perimeter of the rectangle as a function of the length l of one of its sides. p(l) = sta
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a) The area of a rectangle is calculated by multiplying the length by the width:
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This formula allows us to express the width in terms of area and length. By dividing A by l, we find
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b)
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4 months ago
If NO = 17 and NP = 5x -6, find the value of x. Then find NO and OP.
Zina [12379]
Assuming that NO equals NP, we can set up the equation 17 = 5x - 6. To find x, we add 6 to both sides, resulting in 23 = 5x. I'm not sure if the answer should be in decimal form, but dividing 23 by 5 gives 4.6. Therefore, x equals 4.6. Substituting this back, we find NO = 17 and NP = 17, which I believe is the solution to the problem. Please let me know if this is correct.
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3 months ago
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