Mathematics, 14.02.2020 01:06 batmanmarie2004

It is said that sufferers of a cold virus experience symptoms for 7 days. However, the amount of time is actually a normally distributed random variable whose mean is 7.5 days and whose standard deviation is 1.2 days.

a. What proportion of cold sufferers experience fewer than 4 days of symptoms?
b. What proportion of cold sufferers experience symptoms for between 7 and 10 days?

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Answer from: floreschachi2873

a) 0.18% of cold sufferers experience fewer than 4 days of symptoms

b) 64.40% of cold sufferers experience symptoms for between 7 and 10 days.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 7.5, \sigma = 1.2$

a. What proportion of cold sufferers experience fewer than 4 days of symptoms?

This is the pvalue of Z when X = 4. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{4 - 7.5}{1.2}$

Z = -2.92

Z = -2.92 has a pvalue of 0.0018.

So 0.18% of cold sufferers experience fewer than 4 days of symptoms.

b. What proportion of cold sufferers experience symptoms for between 7 and 10 days?

This is the pvalue of Z when X = 10 subtracted by the pvalue of Z when X = 7. So

X = 10

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{10 - 7.5}{1.2}$

Z = 2.08

Z = 2.08 has a pvalue of 0.9812.

X = 7

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{7 - 7.5}{1.2}$

Z = -0.42

Z = -0.42 has a pvalue of 0.3372.

So 0.9812 - 0.3372 = 0.644 = 64.40% of cold sufferers experience symptoms for between 7 and 10 days.

Answer from: Quest

fahrenheit

step-by-step explanation:

fahrenheit is more precise than celsius. the ambient temperature on most of the inhabited world ranges from -20 degrees fahrenheit to 110 degrees fahrenheit—a 130-degree range. on the celsius scale, that range is from -28.8 degrees to 43.3 degrees—a 72.1-degree range. this means that you can get a more exact measurement of the air temperature using fahrenheit because it uses almost twice the scale.

Answer from: Quest

answer: 0

step-by-step explanation: the positive, like 5, + its opposite, like -5 would be 0

5+(-5)=0, or 5-5=0

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