The amount of time a bank teller spends is normally distributed with each customer has a population mean of 3.10 minutes and standard deviation of 0.4 minutes. Assume you select a random sample of 16 customers.
a. What is the probability that the sample mean time spent per customer is more than 3
minutes?
b. What is the time less than which the sample mean will be with 85% chance?
c. What is the range in which the sample mean will be with 90% chance?
d. If you select a random sample of 64 customers, what is the time less than which the
sample mean will be with 85% chance? Explain why your answer is different from that
of part (b).
statistic problem! help pls!
2009-06-09 7:41 am
回答 (2)
2009-06-09 6:27 pm
✔ 最佳答案
Let X be the random variable of the time spent by a bank teller.X bar ~ N(3.10 , 0.42/16)
X bar ~ N(3.10 , 0.12)
a. P(X bar > 3)
= P[z > (3 - 3.10)/0.1]
= P(z > -1)
= 0.5 + 0.3413
= 0.8413
b. Let C be the time required
P(X bar < C) = 0.85
P[z < (C - 3.10)/0.1] = 0.85
(C - 3.10)/0.1 = 1.03652
C = 3.2037 mins
c. This is asking the 90% confidence interval.
The 90% confidence interval
= [3.10 +- 1.645(0.1)]
= (2.9355 , 3.2645)
So, the range of the sample mean is 2.9355 mins to 3.2645 mins.
d. Now, X bar ~ N(3.10 , 0.42/64)
X bar ~ N(3.10 , 0.052)
Let C be the time required
P(X bar < C) = 0.85
P[z < (C - 3.10)/0.05] = 0.85
(C - 3.10)/0.05 = 1.03652
C = 3.1518 mins
which is less than the time found in part (b). It is because moresamples are collected, so a more precise statistics can be found. Thatis, the sample mean is more tended to the population mean.
參考: Physics king
2009-06-10 4:09 am
that's perfect. Thx u so much!!
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