he amount of corn chips dispensed into a 12-ounce bag by the dispensing machine has been identified as possessing a normal dist
ribution with a mean of 12.5 ounces and a standard deviation of 0.2 ounces. Suppose 100 bags of chips were randomly selected from this dispensing machine. Find the probability that the sample mean weight of these 100 bags exceeded 12.6 ounces. Round to four decimal places.
1 answer:
Answer:
The probability will be 0.3085 or 0
Step-by-step explanation:
Given:
True mean=12.5
Sample mean =12.6
Standard deviation=0.2
Samples=100
To Find:
Probability that exceeds 12.6 ounces.
Solution:
Calculate the Z-score for given means and standard deviation.
So
Z-score= (true mean -sample mean)/standard deviation.
Z-score=(12.5 -12.6)/0.2
=-0.1/0.2
=-0.5
Now Using Z-table
P(X≥-0.5)=p(Z≥-0.5)=0.3085
Hence Probability that sample mean weight exceeds will be 0.3085
OR
By using Normal distribution with sampling ,it will be as follows
Z=(X-u)/[Standard deviation/Sqrt(No of samples)]
Z=(12.6-12.5)/(0.2/Sqrt(100)
Z=0.1/0.2/10
Z=5
So P(X≥12.6 )=P(Z≥5)=1
Pr(Z≥5)=1-1=0.
(Refer the attachment )
Hence Probability of getting ounces greater than 12.6 is '0'.
The sampling is of 0.02 size hence graphically it looks likely.
as shown in attachment.
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Complete Question
The complete question is shown on the first uploaded image
Answer:
The optimal point(i.e the position of P) that will allow Sally to reach the cabin as quickly as possible is from the cabin.
Step-by-step explanation:
From the question we are told that
The speed from the point Sally is standing to the point P is
The speed from the point P to the cabin is
Let denote the distance from the bottom left corner to the P be y ft
Generally according to Pythagoras theorem the distance from Sally's first position to point P is mathematically represented as
Generally the distance from that point P to the cabin is mathematically represented as
Generally the time it takes Sally to cover that distance s is mathematically represented as
=>
Generally the time it takes Sally to cover that distance d is mathematically represented as
=>
So the total time taken is
Generally the minimum time taken with respect to the distance is mathematically evaluated by differentiating and equating the derivative to 0
So
=>
=>
=>
=>
So the distance from point P to the cabin is
=>
So the optimal point(i.e the position of P) that will allow Sally to reach the cabin as quickly as possible is from the cabin
