Question

The following data represent the high-temperature distribution for a summer month in a city for some of the last 130 years. Treat the data as a population Complete parts (a) through (c) Temperature 50-59 60-69 70-79 80-89 90-99 100-109 Days 3 310 1412 9 1527 429 (a) Approximate the mean and standard deviation for temperature (Round to one decimal place as needed.) (Round to one decimal place as needed) (b) Use the frequency histogram of the data to verify that the distribution is bell shaped. o 1700- a Yes, the frequency histogram of the data is bell shaped Click to select your answer(s).

Answer 1

Solution:

a)

Class (1) Frequency 0 Mid value (x) (2) X-A x - 84.5 d= h 10 4 = 84.5, h = 10 f.d (5) = (2) x (4) (3) f.de (6) = (5) x (4) 3 54.5 -3 -9 27 50 - 59 60 - 69 310 64.5 -2 -620 1240 70 - 79 1412 74.5 -1 -1412 1412 80 - 89 1527 84.5=A 0 0 0 90 - 99 429 94.5 1 429 429 100 - 109 9 104.5 2 18 36 --- n = 3690 ----- Sf.de - 1594 r. d = 3144 Στα Mean x = A + 71 h = 84.5+ 1594 3690 . 10 = 84.5+ - 0.432 . 10 = 84.5 + - 4.3198 = 80.1802 (Std) M Population Standard deviation o = 12

(-1594), 3144 - 360 3690 10 - 13144 - 688.5734 3690 10 | 2455.4266 3690 10 = 0.6654.10 = 0.8137.10 = 8.1574

b)

The correct option is A

The frequency histogram of the data is bell shaped

c)

Using empirical rule

95% of days in month will be between

95% ≈ M ± 2SD = 80.18 ± 2(8.157) = 63.866 to 96.494