A company introduced a much smaller variant of its tablet, known as the tablet junior. Weighing less than 11 ounces, it was about 50% lighter than the standard tablet. Battery tests for the tablet junior showed a mean life of 9.75 hours. Assume that battery life of the tablet junior is uniformly distributed between 7.5 and 12 hours.
a. Give a mathematical expression for the probablility density function of battery life.
b. What is the probablility that the battery life for the tablet junior will be 9.5 hours or less?

a)

b) 44.44% probablility that the battery life for the tablet junior will be 9.5 hours or less

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The uniform probability distribution has the following density function:

The probability that we find a value X lower than x is given by the following formula.

a)

Assume that battery life of the tablet junior is uniformly distributed between 7.5 and 12 hours.

This means that

b)

44.44% probablility that the battery life for the tablet junior will be 9.5 hours or less

i think it is x = 1.2

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)