Question
In: Statistics and Probability
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined...
Engineers must consider the breadths of male heads when
designing helmets. The company researchers have determined that the
population of potential clientele have head breadths that are
normally distributed with a mean of 7.1-in and a standard deviation
of 1.1-in.
In what range would you expect to find the middle 68% of most head
breadths?
Between_______ and ________
If you were to draw samples of size 48 from this population, in
what range would you expect to find the middle 68% of most averages
for the breadths of male heads in the sample?
Between________ and ________
Enter your answers as numbers. Your answers should be accurate to 2
decimal places.
Solutions
Expert Solution
Solution :
mean = 
= 7.1
standard deviation = 
= 1.1
Using standard normal table,
a ) P(-z < Z < z) = 68%
P(Z < z) - P(Z < z) = 0.68
2P(Z < z) - 1 = 0.68
2P(Z < z ) = 1 + 0.68
2P(Z < z) = 1.68
P(Z < z) = 1.68 / 2
P(Z < z) = 0.84
z = 0.99 znd z = - 0.99
Using z-score formula,
x = z *
+
x = 0.99 * 1.1 + 7.1
= 8.189
x = 8.19
x = z *
+
x = - 0.99 * 1.1 + 7.1
= 6.011
X = 6.01
b ) n = 48
= 7.1
=
/ 
P(-z < Z < z) = 68%
P(Z < z) - P(Z < z) = 0.68
2P(Z < z) - 1 = 0.68
2P(Z < z ) = 1 + 0.68
2P(Z < z) = 1.68
P(Z < z) = 1.68 / 2
P(Z < z) = 0.84
z = 0.99 znd z = - 0.99
Using z-score formula,
= z *
+
= 0.99 * 0.1588 + 7.1
= 7.257
= 7.26
= z *
+
= - 0.99 * 0.1588+ 7.1
= 6.943
= 6.94
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