Question

The mean June midday temperature in Desertville is 36C and the standard deviation is 3C.Assuming this data is normally distributed, how many days in June would you expect the middaytemperature to be between 39C and 42C

Answer 1

4

Explanation:

Given that:

Mean temperature (m) = 36°C

Standard deviation (s) = 3°C

Temperature between 39°C and 42°C

Temperature < 39°

Probability of temperature < 39

P(x < 39)

The standardized score (Z) :

Z = (x - m) / s

Z = (39 - 36) / 3 = 1

p(Z < 1) = 0.84134 ( Z probability calculator)

Temperature < 42°

Probability of temperature < 42°

P(x < 42)

The standardized score (Z) :

Z = (x - m) / s

Z = (42 - 36) / 3 = 2

p(Z < 2) = 0.97725 ( Z probability calculator)

p(Z < 2) - p(Z < 1) = 0.97725 - 0.84134 = 0.13591

Hence, number of days in June = 30

Expected number of days = 30 * 0.13591 = 4.0773 = 4 (nearest whole number)