The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour. Find the probability that it would take between 2.5 and 3.5 hours to construct a soapbox derby car.
A .3085
B .3830
C .6170
D .6915

B

Step-by-step explanation:

In this question, we will be calculating the probability between a range using normal distribution.

We proceed as follows;

we have, mean (μ)= 3 and standard deviation (σ) = 1

P(2.5<X<3.5) = P(2.5 - 3 < X- μm < 3.5 -3) = P( -0.5/1 < (X - μ ) /σ < 0.5/1 )

since Z= (X - μ ) / σ

P(2.5<X<3.5) = P(-0.5 < Z < 0.5)

Using Standard Normal Table or Z-calculator it can be found that ,

P(-0.5 < Z < 0.5) = 0.383

because P(−0.5<Z<0.5 ) = P ( Z<0.5 ) − P (Z<−0.5 )

using Standard Normal Table : P ( Z<0.5 )=0.6915 and P ( Z<−0.5 ) can be found by using the following fomula.

P ( Z<−a)=1−P ( Z<a )

After substituting a=0.5 we have: P ( Z<−0.5)=1−P ( Z<0.5 )

We see that P ( Z<0.5 )=0.6915 so,

P ( Z<−0.5)=1−P ( Z<0.5 )=1−0.6915=0.3085

At the end we have: P (−0.5<Z<0.5 )= P ( Z<0.5 ) − P (Z<−0.5 ) = 0.383

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.

18.75 gallons

step-by-step explanation: