Respuesta :
Answer:
The probability that the mean life a random sample of 25 such blenders falls between 4.6 and 5.1 years is 0.6687.
Step-by-step explanation:
We have given :
The average life a manufacturer's blender is 5 years i.e. [tex]\mu=5[/tex]
The standard deviation is [tex]\sigma=1[/tex]
Number of sample n=25.
To find : The probability that the mean life falls between 4.6 and 5.1 years ?
Solution :
Using z-score formula, [tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The probability that the mean life falls between 4.6 and 5.1 years is given by, [tex]P(4.6<X<5.1)[/tex]
[tex]P(4.6<X<5.1)=P(\frac{4.6-5}{\frac{1}{\sqrt{25}}}<Z<\frac{5.1-5}{\frac{1}{\sqrt{25}}})[/tex]
[tex]P(4.6<X<5.1)=P(\frac{-0.4}{\frac{1}{5}}<Z<\frac{0.1}{\frac{1}{5}})[/tex]
[tex]P(4.6<X<5.1)=P(-2<Z<0.5)[/tex]
[tex]P(4.6<X<5.1)=P(Z<0.5)-P(Z<-2)[/tex]
Using z-table,
[tex]P(4.6<X<5.1)=0.6915-0.0228[/tex]
[tex]P(4.6<X<5.1)=0.6687[/tex]
Therefore, the probability that the mean life a random sample of 25 such blenders falls between 4.6 and 5.1 years is 0.6687.
