High School

The daily high temperatures in a vacation resort city are approximately normal, with a mean temperature of 75 degrees Fahrenheit and a standard deviation of 6 degrees. What percentage of days have a high temperature between 66 and 80 degrees?

Answer :

72.99% of days have a high temperature between 66 and 80 degrees.

Let random variable x denote the daily temperature in a variation resort city.

then E(x) = μ = 75

and S.D. = √var(x) = σ = 6

x is approximately normal

x ≈ N(75, 6²)

then Z = (X - 75) / 6

Z ~ N(0,L)

P(66< x < 80) = P((66-75 / 6) < (x - 75 / 6) < 20 - 75 / 6)

= P( -1.5 < z < 0.23), where Z = (x - 75 / 6)

=P(z<0.23) - P(z ≤ -1.5)

= 0.7967 - 0.0668

= 0.7299

P(66< x < 80) = 0.7299

Therefore, 72.99% of days have a high temperature between 66 and 80 degrees.

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