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The daily high temperature in Winnipeg during the month of January is known to followa normal distribution with a mean of20C. It is also known that 95% of all daily hightemperatures in Winnipeg during the month of January are between32C and8C.What is the approximate value of?

(A) 3C(B) 4C(C) 6C(D) 8C(E) 12C

Respuesta :

Answer:

Option C) 6C

Step-by-step explanation:

We are given the following in the question:

Mean, μ = 20C

Empirical Formula:

  • Almost all the data lies within three standard deviation from the mean for a normal data.
  • Around 95% of the data lies within 2 standard deviations of the mean.

Thus, we can write:

[tex]P(32C < x < 8C) = 95\%\\\mu + 2\sigma = 32C\\\mu - 2\sigma = 8C[/tex]

Putting the value in the equation, we get,

[tex]20C + 2\sigma = 32C\\2\sigma = 12C\\\sigma = 6C[/tex]

Thus, the approximate value for standard deviation is

Option C) 6C

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