Before every flight the pilot must verify that the total...

Before every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 36 passengers, and a flight has fuel and baggage that allows for a total passenger load of 5,796 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 5,796 lbs / 36=161 lb. What is the probability that the aircraft is overloaded? Should the pilot take any action to correct for an overloaded aircraft? Assume that weights of men are normally distributed with a mean of 181.1 lb and a standard deviation of 37.3. The probability is approximately ___. (Round to four decimal places as needed.

Transcript

00:01 So for this question, let's see what we got here.

00:03 Before every flight, the pilot must verify the total weight of the load is less than a maximum allowable load for an aircraft.

00:11 So it can't be overloaded.

00:13 This aircraft can hold 36 passengers.

00:16 It can carry fuel and baggage, and it allows for a total load of 5 ,796 pounds.

00:23 The pilot looks it over, sees it full of men.

00:27 The aircraft will be overloaded if the mean weight of the passengers is greater than.

00:34 They take the weight divided by 36, which is 161 pounds.

00:38 So if each person weighs 161 or over, we're overloaded.

00:43 So what's the probability that the aircraft is overloaded? should the pilot take action to correct? so here's our question.

00:51 What's the probability it's overloaded? should the pilot take action to correct for the overloaded aircraft? so there are a lot of numbers in here, but here's the main thing.

01:03 We're assuming the weights of men are normally distributed.

01:08 So when they say you can normally, it's normally distributed, it follows the bell shape curve or a normal distribution.

01:17 It also, it should tell us the mean, and it should tell us a standard deviation, which it does.

01:22 It tells us a mean of 181 and a standard deviation of 37 .3.

01:27 So if we take that, those two numbers, okay, we're going to put that into our standard deviation curve here.

01:35 So this in the standard and this normal curve i mean the normal curve in the middle goes the mean which is 181 pounds 181 .1 pounds okay now to get the next numbers here we're going to add 37 .3 and then to get the other numbers behind it we're going to take away 37 .3 the standard deviation so i've set up in my calculator a well it was going to be really fast okay so if i take away let's do the adding part first because it's a little bit easier to see.

02:23 So if i add 27 .3 as i move forward here, use green as i move forward here, that first steering deviation is going to correlate to a number of 218 .4.

02:38 All i'm doing is just adding, okay? i'm just taking 181 .1 plus 37 .3, which is the standard deviation to 18 .14.

02:49 Add it again.

02:50 Add 37 .3.

02:55 255 .7 add it again.

03:00 Of course hit the right buttons.

03:09 Okay.

03:11 Now take it away.

03:12 So you can see why i had this table.

03:14 If i take away the 37 .3 and if i'm going backwards now, if i take it away, if i'm going to the minus one standard deviation is 143 .8.

03:25 And if i take it away again, i get 106 .5.

03:29 If i take it away again, i get 69 .5.

03:32 I'm sorry, 69 .2.