Answer: 0.0075
Step-by-step explanation:
Given : The manufacturer of cans of salmon that are supposed to have a net weight of 6 ounces tells you that the net weight is actually a normal random variable with
[tex]\mu=5.99\text{ ounces}[/tex]
[tex]\sigma=0.21\text{ ounces}[/tex]
Sample size : n=43
Z-score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= 5.98
[tex]z=\dfrac{5.48-5.99}{0.21}\approx-2.43[/tex]
By using standard normal distribution table table , the probability that the mean weight of the sample is less than 5.98 ounces will be :_
[tex]P(x<5.98)=P(z<-2.43)=0.0075494\approx0.0075[/tex]
Hence, the probability that the mean weight of the sample is less than 5.98 ounces = 0.0075
