Answer :
Basically we have to calculate P X < 0.95. By using the normal distribution formula for any random variable we can get our answer.
SO first from z table we will have to check the corresponding z value from the table. After we get that value we can do X - mean / the std dev = that particular value that i am naming A.
SO X - 5 / 0.5 = A. Now we can solve X for our answer.
Answer:
The range that 95% of the bags fall within is (4.02,5.98)
Step-by-step explanation:
Given : A potato sorting machine produces 5 lb bags of potatoes on average, but the standard deviation is 1/2 lb. Assuming that the weight of the bags is normally distributed
To find : How you would find the weight range that 95% of the bags fall within?
Solution :
We have given,
Mean is [tex]\mu=5[/tex]
Standard deviation is [tex]\sigma=\farc{1}{2}=0.5[/tex]
The critical value for a 95% confidence interval is 1.96.
Let x=1.96
The formula to find the range or confidence interval is
[tex]\mu-x\sigma\leq CI\leq \mu+x\sigma[/tex]
Substitute the value in the formula,
[tex]5-1.96\times 0.5\leq CI\leq5+1.96\times 0.5[/tex]
[tex]5-0.98\leq CI\leq5+0.98[/tex]
[tex]4.02 \leq CI \leq 5.98[/tex]
Therefore, The range that 95% of the bags fall within is (4.02,5.98)
