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# hw3_1 - and standard deviation of 0.05mm A random sample of...

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Homework 3 (due Feb. 11) 1. Suppose a continuous random variable X is distributed uniformly on the interval [20 , 30]. An analyst does not know the interval (although believes that the distribution is uniform), and tries to estimate it (or, more precisely, its endpoints), using MLE. Using Excel as a simulation tool, run this experiment 10 times for each of the following sample sizes: 5, 10, 50. Record the resulting estimated intervals. Compute the observed average biases for a and b for all three sample sizes. What do you observe? 2. Ball bearing diameters are normally distributed with the mean of 5mm
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Unformatted text preview: and standard deviation of 0.05mm. A random sample of size 20 is taken. Find the probability that the sample mean lies between 4.98mm and 5.02mm. 3. In the previous problem, ﬁnd the probability that the sample standard deviation is between 0.03mm and 0.07mm. 4. Suppose 70% of all potential customers prefer cars with a sunroof to the ones without. If the company decides to randomly poll 200 people, what is the probability that the sample percentage of sunroof lovers turns out to be below 60%? 1...
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