A certain delivery truck carries loads that follow a normal distribution with an average weight of 3500 pounds and a standard deviation of 700 pounds.  For the following, show your graph and calculator commands.What load weight represents the top 30% of loads?What proportion of loads are less than 3000 pounds? What two load weights hold the middle 80% of loads? Find the 90th percentile of load weights. If a load is more than 6000 pounds, it is considered unsafe. What proportion of loads were unsafe? Using probability, would it be unusual for the delivery truck to carry an unsafe load?

Question
Asked Oct 12, 2019

A certain delivery truck carries loads that follow a normal distribution with an average weight of 3500 pounds and a standard deviation of 700 pounds.  For the following, show your graph and calculator commands.

  1. What load weight represents the top 30% of loads?
  2. What proportion of loads are less than 3000 pounds? 
  3. What two load weights hold the middle 80% of loads? 
  4. Find the 90th percentile of load weights. 
  5. If a load is more than 6000 pounds, it is considered unsafe. What proportion of loads were unsafe? Using probability, would it be unusual for the delivery truck to carry an unsafe load?  
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The load weight that represents the top 30% of loads is 3,867.1 pounds, shown in the graph below.

The first ...

Normal Distribution
Overlay
Ок
C calculate P given X
calculate X given P
P
.3
Clear
Cancel
mean
3500
standard deviation
700
Help
Shading
Color
Show axis points
Sold color
Clower
Show center line
upper
Transparent
Patterned
pwo-tail
Axis labels
C No shading
Rounding
none
4,200.0
4,900.0
1,400.0
2,100.0
2,800.0
3,500.0
5,600.0
3,867.1
Normal distribution
Plower) Plupper)
mean std.dev
z
7000
700 0
3000
0.52 3,867.1 3,500.0
help_outline

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Normal Distribution Overlay Ок C calculate P given X calculate X given P P .3 Clear Cancel mean 3500 standard deviation 700 Help Shading Color Show axis points Sold color Clower Show center line upper Transparent Patterned pwo-tail Axis labels C No shading Rounding none 4,200.0 4,900.0 1,400.0 2,100.0 2,800.0 3,500.0 5,600.0 3,867.1 Normal distribution Plower) Plupper) mean std.dev z 7000 700 0 3000 0.52 3,867.1 3,500.0

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