Clinic took temperature reading of 250 flu patients over a weekend and discovered the temperature distribution to be Gaussian with a mean of 101.40 degree F and a slandered deviation of 0.8890
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The question is not complete. So it is not possible to give numerical answers. However, I will mention the procedure to solve this type of questions.
N = 250
μ = 101.40 °C
σ = 0.8890 °C
Problem 1)
Suppose we want to know the number of patients having a temperature more than 102.5 °C, then we do as here.
Z = (102.5 - 101.40) / 0.8890 = 1.2373
We use the standard Normal tables that give the cumulative probability for Gaussian population distribution.
P(0 <= Z <= 1.2373) ≈ 0.391
So P(Z > 1.2373) = 0.50 - 0.391 = 0.109
Now to obtain the number of patients with temperature above 102.5°C,
n = 250 * 0.109 = 27.25 or let us say 28 patients.
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2) We suppose want to know the number of patients having temperature between 100.5°C and 102.5°C, then we do as the following.
Z1 = (101.40 - 100.5) / 0.8890
Z2 = (102.5 - 101.40) / 0.8890
Now find P(0 <= Z <= Z1) + P(0 <= Z <= Z2) using the standard Z tables or Normal tables. Then multiply that by N.
N = 250
μ = 101.40 °C
σ = 0.8890 °C
Problem 1)
Suppose we want to know the number of patients having a temperature more than 102.5 °C, then we do as here.
Z = (102.5 - 101.40) / 0.8890 = 1.2373
We use the standard Normal tables that give the cumulative probability for Gaussian population distribution.
P(0 <= Z <= 1.2373) ≈ 0.391
So P(Z > 1.2373) = 0.50 - 0.391 = 0.109
Now to obtain the number of patients with temperature above 102.5°C,
n = 250 * 0.109 = 27.25 or let us say 28 patients.
=======
2) We suppose want to know the number of patients having temperature between 100.5°C and 102.5°C, then we do as the following.
Z1 = (101.40 - 100.5) / 0.8890
Z2 = (102.5 - 101.40) / 0.8890
Now find P(0 <= Z <= Z1) + P(0 <= Z <= Z2) using the standard Z tables or Normal tables. Then multiply that by N.
kvnmurty:
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