Question

Suppose a new climate is heading toward both a higher average temperature and greater variation. Statistically represented here with the graph showing a higher mean and greater variation.

Climate Change 3 Let the old climate (solid curve) have a mean value of 14o C (that is 57.2o F) with a standard deviation of 10o C . Find z-scores for the data values of interest below using the formula: z-score = data value - mean standard deviation and then find the percentages requested using either a normal distribution table or a capable calculator. Use one year = 365 days. Round all percents to the nearest tenth of a percent and all days to the nearest day.

a) What percent of days will be 34o C or higher? % (nearest tenth of a percent)

b) How many days out of a year would that be? 8 Correct (nearest day)

c) What percent of days will be -6o C or lower? 0.4772 % (nearest tenth of a percent) Now let the new climate (dashed curve) have a mean value of 16o C (a higher average), with a standard deviation of 12o C (greater variation). Find the new z-scores and the new percentages for those same temps:

e) What percent of days will be 34o C or higher? 6.68 Incorrect % (nearest tenth of a percent)

f) How many days out of a year would that be? 24 Correct (nearest day) g) What percent of days will be -6o C or lower? 24 Incorrect % (nearest tenth of a percent)

h) How many days out of a year would that be? 12 Correct (nearest day) Explain why there were more cold days even though the average temperature increased.: There were more cold days even though the average temperature increased because the standard deviation of new climate = 12 is more than standard deviation of Old climate = 10

Answer 1

1)

Mean, = 14 °C

Standard deviation, = 10 °C

(a) Z value corresponding to 34 °C = (34 - 14)/10 = 2

Percentage of days with 34 °C or higher = P(Z ≥ 2) = 2.28%

(b) Number of days in the year = 0.0228*365 = 8.322 ≈ 8 days

(c) Z value corresponding to -6 °C = (-6 - 14)/10 = -2

Percentage of days with -6 °C or lower = P(Z ≤ - 2) = 2.28%

(d) Number of days in the year = 0.0228*365 = 8.322 ≈ 8 days

New mean = 16 °C

New Standard deviation = 12 °C

(e) Z value corresponding to 34 °C = (34 - 16)/12 = 1.5

Percentage of days with 34 °C or higher = P(Z ≥ 1.5) = 6.68%

(f) Number of days in the year = 0.0668*365 = 24.382 ≈ 24 days

(g) Z value corresponding to -6 °C = (-6 - 16)/12 = -1.833

Percentage of days with -6 °C or lower = P(Z ≤ - 1.833) = 3.34%

(h) Number of days in the year = 0.0334*365 = 12.191 ≈ 12 days