The probability that the aircraft is overloaded is 0.6141; since this is a greater than 50% chance, the pilot should either reduce the number of passengers on the plane or require them to reduce their baggage.
The z-score for this is given by
z = (X-μ)/σ = (169-180.2)/38 = -11.2/38 = -0.29.
Using a z-table (http://www.z-table.com) we see that the probability of weights being less than this (the area to the left of this score) is 0.3859; to find the probability that the weight is greater than this (to the right), we subtract from 1:
1-0.3859 = 0.6141.
(a+b)^7= a^7+ 7a^7b+ 21 a^6b²+ 35a^5b³+ 35 a⁴b⁴+ 21 a³b^5 + 7a²b^6 + b^7
