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lapo4ka [179]
2 years ago
13

The time at which the mailman delivers the mail to ace bike shop follows a normal distribution with mean 2:00 pm and standard de

viation of 15 minutes.
Mathematics
1 answer:
ivolga24 [154]2 years ago
4 0

There are three questions related to this problem.


First, the probability of the mail will arrive after 2:30 PM


<span>Find the z-score of 2:30 which is 30 minutes after 2:00.</span>

<span>
z(2:30) = (2:30 – 2:00)/15 = -30/15 = -2</span>

<span>
P(x < 2:30) = P(z<-2) = 0.0228</span>

<span>
</span>

Second, the probability of the mail will arrive at 1:36 PM

<span>Find the z-score of 1:36 which is 24 minutes before 2:00.</span>

<span>
z(1:36) = (1:36 – 2:00)/15 = -24/15 = -1.6</span>

<span>
P(x < 1:36) = P(z<-1.6) = 0.0548</span>

 

Lastly, the probability of the mail will arrive between 1:48 PM and 2:09 PM


Find the z-score of 1:46 and 2:09 PM which will result to a z value of 0.034599


<span>P(1:48 < x < 2:09) = P(z<0.034599) = 0.5138</span>

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