Question

Studies have shown that honolulu has an average daily temperature of m = 73 f with o = 5�� f. what is the probability that if we fly to honolulu, we'll find the temperature falling:

a. between a nice 70�� f and 80�� f:
b. below 65�� f (that's sweater weather!):
c. above 90�� f:

Answer 1

To find the probability of temperature ranges in Honolulu, we can use the normal distribution and z-scores. The probability of temperatures between 70°F and 80°F is approximately 30.97%. The probability of temperatures below 65°F is approximately 5.16%, and the probability of temperatures above 90°F is approximately 0.02%.

Step-by-step explanation:

To find the probability that the temperature in Honolulu falls within a certain range, we can use the standard normal distribution. First, we need to convert the given temperature values to z-scores using the formula z = (x - mean) / standard deviation. Then, we can use a z-table to find the probabilities.

a. Between 70°F and 80°F:

Convert 70°F and 80°F to z-scores:

z1 = (70 - 73) / 5 = -0.6

z2 = (80 - 73) / 5 = 1.4

Using the z-table, we find that the probability is P(-0.6 < Z < 1.4) = 0.5840 - 0.2743 = 0.3097, or 30.97%.

b. Below 65°F:

Convert 65°F to a z-score:

z = (65 - 73) / 5 = -1.6

Using the z-table, we find that the probability is P(Z < -1.6) = 0.0516, or 5.16%.

c. Above 90°F:

Convert 90°F to a z-score:

z = (90 - 73) / 5 = 3.4

Using the z-table, we find that the probability is P(Z > 3.4) = 1 - 0.9998 = 0.0002, or 0.02%.