Question

The mean voltage of a battery is 15 and s.d is 0.2. find the probability that four such batteries connected in series will have a combined voltage of 60.8 or more volts

Answer 1

Step-by-step explanation:

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Answer 2

Concept

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes.

Given

We have given mean voltage of battery 15 and standard deviation 0.2

and combined voltage of 60.8 when connected in series .

Find

We are asked to find determine probability of four batteries when connected in series .

Solution

Let mean voltage of batteries A,B,C,D be $\bar X_A \ , \bar X_B \ , \bar X_C \ , \bar X_D$ .

The mean of the series of the series of the four batteries connected is

$\mu_{\bar X_A+ \bar X_B +\bar X_C +\bar X_D} =\mu_{\bar X_A} +\mu_{\bar X_B}+\mu_{\bar X_C}+\mu_{\bar X_D$

                           $15+15+15+15=60$

$\sigma_{A+B+C+D}=\sqrt{\sigma^2_{A} +\sigma^2_{B}+\sigma^2_{C}+\sigma^2_{D} }$

                   $\sqrt{4(0.2)^2}=0.4$

Let X be the combined voltage of the series

When x = 60 ,$z=\frac{x-\mu}{\sigma} =\frac{60.8-60}{0.4} =2$

Then the probability combined voltage is more than is more than 60.8 is given by

$P(X\ge 60.8)=P(z \ge2)=0.5-0.4772=0.0228$

Therefore, the probability that four such batteries connected in series is 0.0228 .

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