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According to the WHO, the COVID-19 incubation period is between 2 to 14 days. However, according...

According to the WHO, the COVID-19 incubation period is between 2 to 14 days. However, according to a Chinese study published in the New England Journal of Medicine on January 30, the amount of time is a random variable with a mean of 5.2 days and a standard deviation is 2.4 days. What is the probability that the mean incubation period of a randomly sample of 36 confirmed cases does not exceed 6 days?

Math   Statistics-And-Probability   
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Answer #1

Here' the answer to the question. Please let me know in case you've doubts.

Lets use the normal distribution.

P(X<6) = ?

Mean = 5.2 days

Stdev = 2.4 days

The formula for standardizing is : Z = (X-Mean)/(Stdev/sqrt(n))

P(X>6)

= P(Z> (6-5.2)/(2.4/sqrt(30))

= P(Z>1.826)  

Lets use Z tables to convert Z to probability values.

= .0339

Answer: probability that the mean incubation period of a randomly sample of 36 confirmed cases does not exceed 6 daysis 0.0339

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