Fill amounts of jars of peanuts from a certain factors are known to follow a Normal...

Fill amounts of jars of peanuts from a certain factors are known to follow a Normal distribution with mean 454g and standard deviation 15g. Suppose that a random sample of 8 jars is taken. What is the probability that the average weight of this sample is between 451g and 458g?

Solutions

Expert Solution

Solution :

Given that,

mean = = 454

standard deviation = = 15

n = 8

= = 454

= / n = 15/ 8 = 5.30

P(451 < < 458 )

= P[(451- 454) /5.30 < ( - ) / < (458 - 454) /5.30 )]

= P( -0.57< Z < 0.75 )

= P(Z < 0.75) - P(Z < -0.57)

= 0.7734 - 0.2843 = 0.4891

Probability = 0.4891

orchestra answered 1 year ago

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