The life, in years, of a certain type of electrical switch has an exponential distribution with an average life β = 2. if 100 of these switches are installed in dif- ferent systems, what is the probability that at most 30 fail during the first year?

6.75 or 6 3/4 gallons

Step-by-step explanation:

First we can add the whole numbers together: 3 + 2 = 5

Now, we need to add 7/8 + 7/8, this is the same as multiplying 7/8 times 2.

2= 2/1, and we multiply across when multiplying fractions, so it would look like:

7/8 × 2/1=?

For fraction multiplication, multiply the numerators and then multiply the denominators to get

7×2= 14

8×1= 8

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 14 and 8 using

GCF(14,8) = 2

14÷2 = 7

8÷2= 4

The fraction

7/4

is the same as

7÷4= 1.75

Finally we just add 1,75 + 5 = 6.75 or 6 3/4 since 3/4= 0.75