Question

Maria and Ralph are peeling apples. The time it takes Maria to peel an apple is approximately normally distributed with mean 12 seconds and standard deviation 2 seconds. The time it takes Ralph to peel an apple is approximately normally distributed with mean 11 seconds and standard deviation 2.5 seconds. Find the probability that (starting together) Maria finishes her next apple before Ralph: If the first person done always waits for the second person to finish (so that they always start together), Ralph will finish first percent of the time.

Answer 1

Answer:

The probability that Maria finishes her next apple before Ralph is 0.377.

Ralph will finish first percent of the time is 62.3%

Step-by-step explanation:

Consider the provided information.

Maria to peel an apple is approximately normally distributed with mean 12 seconds and standard deviation 2 seconds. The time it takes Ralph to peel an apple is approximately normally distributed with mean 11 seconds and standard deviation 2.5 seconds.

Find the mean and variance of difference of Maria and Ralph.

$\mu=\mu_M-\mu_R$

$\mu=12-1=1$

$\sigma=\sqrt{(2^2+2.5^2)}$

$\sigma=\sqrt{10.25}=3.202$

Therefore,

$P(X<0)=P(\frac{x-\mu}{\sigma}\leq \frac{0-1}{3.2})$

$P(X<0)=P(Z\leq -0.3125)$

$P(X<0)=0.377$

Hence, the probability that Maria finishes her next apple before Ralph is 0.377.

Part (B) Ralph will finish first percent of the time.

To find this subtract the probability of Maria finishes her apple first with 1 and multiply it with 100.

Ralph will finish first (1-0.377)×100 = 0.623×100=62.3%

Hence, Ralph will finish first percent of the time is 62.3%