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Answer :
[tex]z=\dfrac{M-\mu}{\dfrac\sigma{\sqrt n}}\iff 2.00=\dfrac{44-40}{\dfrac{10}{\sqrt n}}\implies \sqrt n=5\implies n=25[/tex]
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Final answer:
To find the number of scores in the sample, we use the formula for the z-score: z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. Plugging in the known values, we can solve for n.
Explanation:
The z-score formula is given by: z = (x - μ) / σ, where x is the sample mean, μ is the population mean, and σ is the population standard deviation. In this case, the sample mean (M) is 44 and the population mean (μ) is 40. The z-score is given as 2.00. Plugging in the values, we have 2.00 = (44 - 40) / σ. Rearranging the formula, we get σ = (44 - 40) / 2.00 = 4 / 2.00 = 2. Therefore, the population standard deviation is 2.
To find the number of scores in the sample, we can use the formula for the z-score: z = (x - μ) / (σ / √n), where n is the sample size. Plugging in the known values, we have 2.00 = (44 - 40) / (2 / √n). Rearranging the formula, we get √n = (44 - 40) / 2.00 / 2 = 2. Therefore, n = (2)^2 = 4. So, there are 4 scores in the sample.
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