The number of potholes in any given 1 mile stretch of freeway pavement in Pennsylvania has a bell-shaped distribution. This distribution has a mean of 56 and a standard deviation of 10. Using the empirical rule, what is the approximate percentage of 1-mile long roadways with potholes numbering between 36 and 86?

97.35%

Step-by-step explanation:

Empirical rule formula states:

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .

From the question, we have the mean of :

Mean of 56 and a standard deviation of 10.

For 36

36 = μ - xσ

36 = 56 - 10x

56 - 36 = 10x

20 = 10x

x = 20/10

x = 2

Hence, the data falls within 2 standard deviation of the mean

Hence, since it is one side,

= 95%

= 47.5%

For 86

86 = μ - xσ

86 = 56 - 10x

56 - 86 = 10x

-30 = 10x

x = -30/10

x = -3

Hence, the data falls within 3 standard deviation of the mean

Hence, since it is 99.7% one side,

= 99.7%

= 49.85%

Hence, we add up

= 47.5% + 49.85%

= 97.35%

The approximate percentage of 1-mile long roadways with potholes numbering between 36 and 86 is 97.35%

4444444444444 i think

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.