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MATH/STAT 203 A - Probability and Statistics I (SP 2025)

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If you take random samples of the same size repeatedly from the same population, and for each sample you construct a 95% confidence interval for the population mean, then about 95% of the intervals should contain the sample mean.
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My patient was watching the news while she was in her hospital room. When I came in to see her and check her vital signs and medications, she asked: What does Dr. Henry mean with "the false negative rate of Covid-19 tests can be as high as 30%"? I explained to her that she means:
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The anual income of single adults in Canada is normally distributed with a mean of $45,000 and a standard deviation of $10,000. It the z-score of the income of an individual is 3.5 then 

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The length of a pregnancy is normally distributed with mean 268 days and standard deviation 15 days. What is more likely to find?

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Consider a weighted coin with 29% probability of landing heads. 

If this coin is tossed 5 times, what is the probability of getting exactly 2 heads?

Enter your answer as a decimal number.

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Identify the type of sampling that is used in the following scenario. -- In order to find out whether vaccinations depends on race a sample is collected as follows: four ethnic groups are selected at random and a sample from each is included in the study. --

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In a test for one population mean, if the null hypothesis is rejected when the alternative hypothesis is true then:

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If the confidence level of a CI increases then the value of the multiplier

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If the standard deviation of a normal distribution increases then
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The anual income of single adults without a university degree in Canada is normally distributed with a mean of $35,000 and a standard deviation of $10,000. The average rent of a 1-bedroom condo in the Lower Mainland is about $1,500 a month. In addition the average cost of utilities (Internet, Heat, Hydro) is about $300 a month. What proportion of single individual will not be able to afford their rent and utilities?  

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