Men\'s weights are normally distributed with a mean weight of 172 pounds and a s
ID: 3326823 • Letter: M
Question
Men's weights are normally distributed with a mean weight of 172 pounds and a standard deviation of 29 pounds. The engineering firm of Ashley and Joel was 10. hired to design an elevator for the Centerport shopping mall and it must safely carry 16 people. Assuming a worst-case scenario of 16 male passengers find the maximum total allowable weight if we want a .975 probability that this maximum WI will not be exceeded when 16 males are randomly selected? Knowing that x has a normal distribution. Find the area under the normal curve, 15. given (405 x 60), = 30 and = 14.Explanation / Answer
Result:
10).
Total weight of 16 males follows normal with mean 16*172=2752 and with standard deviation 16*29 =464.
Z value for p =0.975 or upper tail p=0.025 is 1.96
z=(x-µ)/
1.96=(x-2752)/464
x=3661.44
The required weight = 3661.44 pounds.
15).
Z value for 40, z =(40-30)/14 = 0.71
Z value for 60, z =(60-30)/14 = 2.14
P( 30 x 60) =p( 0.71<z <2.14)
P( z < 2.14) – P( z < 0.71)
=0.9838 - 0.7611
=0.2227