1 Blast shields are going to be placed 10 feet from an explo

1) Blast shields are going to be placed 10 feet from an explosion. The amount of radiation the shield will absorb is N(7, 1.2²) J/kg.

What is the probability that a randomly placed shield will absorb more than 9 J/kg?

What is the probability that an average of 6 shields will absorb more than 9 J/Kg?

Solution

Here, I assume you use the convention N(mean, sigma^2), so I will treat sigma = 1.104536102.

a)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    9      
u = mean =    7      
          
s = standard deviation =    1.104536102      
          
Thus,          
          
z = (x - u) / s =    1.81071492      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.81071492   ) =    0.035092496 [ANSWER]

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B)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    9      
u = mean =    7      
n = sample size =    6      
s = standard deviation =    1.1045361      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    4.435327633      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   4.435327633   ) =    0.00000459662 [ANSWER]