The lifespan of a lion in a particular zoo are normally distributed. The average lion lives 12.5 years the. Standard deviation is 2.4 years. Use the empirical rule(68-95-99.7%) to estimate the probability of a lion living between 5.3 and 10.1 years.

0.1585

Step-by-step explanation:

Solution:-

The lifespan of a lion in a particular zoo is normally distributed with average lion lives:

                    Mean u = 12.5 years

                    Standard deviation s = 2.4 years

We are to use the empirical rule ( 68-95-99.7% ) to estimate the probability of a lion living between 5.3 and 10.1.

- The empirical rule ( 68-95-99.7% ) states:

                     P ( u - s < X < u + s ) = 68%

                     P ( u - 2s < X < u + 2s ) = 95%

                     P ( u - 3s < X < u + 3s ) = 99.7%

- The test have the following number of standard deviations (s):

                    u - s < X < u + s  = 12.5 - 2.4 < X < 12.5 + 2.4  = 10.1 < X < 14.9

                    u - 2s < X < u + 2s = 12.5 - 4.8 < X < 12.5 + 4.8  = 7.7 < X < 17.3

                    u - 3s < X < u + 3s = 12.5 - 7.2 < X < 12.5 + 7.2  = 5.3 < X < 19.7

Hence,

                   P ( 10.1 < X < 14.9 ) = 0.68

                   P ( 7.7 < X < 17.3 ) = 0.95

                   P ( 5.3 < X < 19.7 ) = 0.997

-  We need P ( X < 10.1 ) and P ( X < 5.3 ):

                  P ( X < 10.1 ) = [ 1 - P ( 10.1 < X < 14.9 ) ] / 2

                                      = [ 1 - 0.68 ] / 2

                                      = 0.16

                  P ( X < 5.3 ) = [ 1 - P ( 5.3 < X < 19.7 ) ] / 2

                                      = [ 1 - 0.997 ] / 2

                                      = 0.0015

Hence,

                 P ( 5.3 < X < 10.1 ) = P ( X < 10.1 ) - P ( X < 5.3 )

                                               = 0.16 - 0.0015

                                               = 0.1585

15.85%

Step-by-step explanation: Answer on Khan

eve and marks ratios are equivalent

step-by-step explanation:

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.