Customers in a Bank In the Ames International Campus Bank (open 24h every day) 5 customers arrive on average during an hour. Ans
wer the following questions. First write down the problem in terms of some random variables and write down what distribution assumptions you make about these random variables. (a) What is the probability that during an hour no customer arrives? (b) What is the probability that during an hour, 7 or more customers arrive? (c) What is the probability that there's more than 30 minutes between the 2nd and 3rd customer of the day? (d) What is the probability that you have to wait less than an hour for seven customers to arrive? (e) How many minutes do you expect to wait until the 12th customer arrives? (f) How many minutes do you expect to wait on average between arrivals?
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Answer:
We conclude that the mean Ohio score is below the national average.
Step-by-step explanation:
We are given that a random survey of 1000 students nationwide showed a mean ACT score of 21.1. Ohio was not used.
A survey of 500 randomly selected Ohio scores showed a mean of 20.8. The population standard deviation is 3.
<u><em>Let </em></u><u><em> = mean Ohio scores.</em></u>
So, Null Hypothesis, :
21.1 {means that the mean Ohio score is above or equal the national average}
Alternate Hypothesis, :
< 21.1 {means that the mean Ohio score is below the national average}
The test statistics that would be used here <u>One-sample z test statistics</u> as we know about population standard deviation;
T.S. = ~ N(0,1)
where, = sample mean Ohio score = 20.8
= population standard deviation = 3
n = sample of Ohio = 500
So, <u><em>test statistics</em></u> =
= -2.24
The value of z test statistics is -2.24.
<em>Now, at 0.1 significance level the z table gives critical value of -1.2816 for left-tailed test.</em><em> Since our test statistics is less than the critical values of z as -2.24 < 1.2816, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which </em><em><u>we reject our null hypothesis</u></em><em>.</em>
Therefore, we conclude that the mean Ohio score is below the national average.