Question

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

Answer 1

Answer:

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