Tanker trucks are designed to carry huge quantities of gasol

Tanker trucks are designed to carry huge quantities of gasoline from refineries to filling stations. A factory that manufactures the tank of the trucks claims to manufacture tanks with a capacity of 8550 gallons of gasoline. The actual capacity of the tanks is normally distributed with mean = 8544 gallons and standard deviation = 12 gallons. Use this information to answer A. a simple random sample of tanks will be selected. Find the z-score corresponding to a sample mean capacity for 20 tanks of 8550. Round your answer to three decimal places. Z= B. A simple random sample of tanks will be selected. What is the probability that the mean capacity for these 50 tanks will be greater than 8540 gallons? Round your answer to three decimal places.

Solution

a)

As

z = (X - u) * sqrt(n) / sigma

Then

z = (8550 - 8544) * sqrt(20) / 12

z = 2.236067977 [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 =    8540      
u = mean =    8544      
n = sample size =    50      
s = standard deviation =    12      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -2.357022604      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -2.357022604   ) =    0.990788937 [ANSWER]