12 points! Please Help!
2 answers:
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Answer:
Binomial; \mu p=87.5, \sigma p=7.542
Step-by-step explanation:
- a distribution is said be a binomial distribution iff
- The probability of success of that event( let it be p) is same for every trial
- each trial should have 2 outcome : p or (1-p) i.e, success or failure only.
- there are fixed number of trials (n)
- the trials are independent
- here, the trials are obviously independent ( because, one person's debt doesn't influence the other person's)
- here n=250
- the probability of success(0.35) is same for every trial
(35/100=0.35 is the required p here)
[since, the formula for ]
[since, the formula for [tex]\sigma _{p} =\sqrt{n*(p)*(1-p)}
- therefore, it is Binomial; \mu p=87.5, \sigma p=7.542
Answer:
Given that the manufacturers claim is true, the probability that the sample mean area is 249.6 ft.² or less is 0.42074
Step-by-step explanation:
The manufacturer claims that mean amount of foil on each roll, μ = 250 ft²
The standard deviation of the measured amount of foil per roll, σ = 2 ft.²
The number of rolls tested by the restaurant, n = 10 rolls
The mean measured by the restaurant, = 249.6
Taking the sample means as individual score, we have;
The z-score, of the sample mean is given as follows;
At = 249.6, we have;
z = (249.6 - 250)/2 = -0.2
Therefore, the probability for a mean less than or equal to 249.6, we have;
The probability, P = P(z < -0.2) = 0.42074
The probability that the sample mean area is 249.6 ft.² or less given that the manufacturers claim is true, P = 0.42074.