Mattel Coroporation produces a remote-controlled car that requires three AA batt
ID: 3024137 • Letter: M
Question
Mattel Coroporation produces a remote-controlled car that requires three AA batteries. The mean life of these batteries in this product is 35.0 hours. The distribution of the battery lives closely follows the normal probability distribution with a standard deviation of 5.5 hours. As part of its testing program Sony tests samples of 25 batteries.
A. What can you say about the shape of the distribution of the sample mean?
B. What is the standard error of the distribution of the sample mean?
C. What proportion of the samples will have a mean useful life or more than 36 hours?
D. What proportion of the sample will have a mean useful life greater than 34.5 hours?
E. What proportion of the sample will have a mean udeful life between 34.5 and 36.0 hours?
Explanation / Answer
Mean ( u ) =35
Standard Deviation ( sd )=5.5
Number ( n ) = 25
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)
a.
It follows a normal distribution with bell shaped curve
b.
stanard error = (sd/Sqrt(n)= 5.5/ Sqrt ( 25 ) = 1.1
c.
P(X > 36) = (36-35)/5.5/ Sqrt ( 25 )
= 1/1.1= 0.9091
= P ( Z >0.9091) From Standard Normal Table
= 0.1817
d.
P(X > 34.5) = (34.5-35)/5.5
= -0.5/5.5 = -0.0909
= P ( Z >-0.091) From Standard Normal Table
= 0.5362
e.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 34.5) = (34.5-35)/5.5
= -0.5/5.5 = -0.0909
= P ( Z <-0.0909) From Standard Normal Table
= 0.46378
P(X < 36) = (36-35)/5.5
= 1/5.5 = 0.1818
= P ( Z <0.1818) From Standard Normal Table
= 0.57214
P(34.5 < X < 36) = 0.57214-0.46378 = 0.1084