Mathematics, 21.02.2020 19:54 karmaxnagisa20

Automobiles traveling on a road with a posted speed limit of 55 miles per hour are checked for speed by a state police radar system. Following is a frequency distribution of speeds.

Speed (miles per hour) 45-49 50-54 55-59 60-64 65-69 70-74 75-79

Frequency 10 40 150 175 75 15 10

Total 475a. What is the mean speed of the automobiles traveling on this road? b. Compute the variance and the standard deviation.

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Answer from: ammyraammirez24

(a) Mean = 60.684

(b) Variance = 31.2292 Standard deviation = 5.5883

Step-by-step explanation:

We are given the following frequency distribution of speeds;

Speed (miles per hour) Frequency (f) X X * f

45-49 10 47 470

50-54 40 52 2080

55-59 150 57 8550

60-64 175 62 10850

65-69 75 67 5025

70-74 15 72 1080

75-79 10 77 770

$\sum f$ = 475 $\sum Xf$ = 28825

(a) Mean speed of the automobiles, Xbar = $\frac{\sum Xf}{\sum f}$ = $\frac{28825}{475}$ = 60.684

(b) Variance formula is given by = $\frac{\sum (X_i - Xbar)^{2} * f }{\sum f - 1}$

This mean variance is given by subtracting each X value from the mean and then squaring each value and then multiplying it with the corresponding frequency.

Variance = $\frac{(47 - 60.684)^{2} * 10 + (52 - 60.684)^{2} * 40 + ......... + (77 - 60.684)^{2} * 10}{475 -1}$

= 31.2292

Standard Deviation = $\sqrt{ Variance}$ = $\sqrt{ 31.2292}$ = 5.5883 .

Answer from: Quest

Google it that might work

Answer from: Quest

answer: finding the extract measurements and knowing the points

step-by-step explanation:

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