Question

A clinic took temperature readings of 250 flu patients over a weekend and discovered the temperature distribution to be Gaussian, with a mean of 102.00°F and a standard deviation of 0.5660. Use this normal error curve area table to find the following values:
(a) What is the fraction of patients expected to have a fever greater than 103.58°F?
(b) What is the fraction of patients expected to have a temperature between 101.43°F and 102.74°F?

Answer 1

Answer:

a) 0.00262 is the fraction of patients expected to have a fever greater than 103.58 F.

b) 0.748 is the fraction of people expected to have temperature between 101.43 F and 102.74 F.

Step-by-step explanation:

We are given the following information:

n = 250

Population mean, μ = 102.00 F

Standard Deviation, σ = 0.5660

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(x > 103.58)

Converting into standard normal variate

$P(z > \displaystyle\frac{103.58 - 102}{0.5660})\\\\= P(z > 2.791)\\= 1 - p(z \leq 2.791)\\= 0.00262$

The probability value is calculated from normal standard table.

Thus, 0.00262 is the fraction of patients expected to have a fever greater than 103.58 F.

b)P(101.43 < x < 102.74)

Converting into standard normal variate

$P(\displaystyle\frac{101.43 - 102}{0.5660} < z < \displaystyle\frac{102.74 - 102}{0.5660})\\\\= P( -1.007 < z < 1.307)\\= P(z < 1.307) - P(z < -1.007)\\= 0.904 - 0.156\\=0.748$

The probability value is calculated from normal standard table.

Hence, 0.748 is the fraction of people expected to have temperature between 101.43 F and 102.74 F.

Answer 2

I get 0.26% for part A and 75% for part B. My work is in the attached document.

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