#### iamalivenow

##### New member

- Joined
- Mar 2, 2018

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**need help w/ "You find a very distant star cluster and measure its mean velocity."**

3 You find a very distant star cluster and measure its mean velocity. You measure the velocities for 12 stars and find a mean velocity of 427.5 km/s for the cluster. You also add up the light, use that to estimate the mass, and from the formulas from Lab 6 you compute the population standard deviation to be 9.4 km/s.

A confidence interval for a measurement is specified by a probability. If we choose 68%, then the 68% confidence interval for a measurement is the range of values that will include the true population value 68% of the time.

3a What is the 95% confidence interval for your measurement? What range of velocities will contain the true population value 95% of the time?

3b You measure the velocities of 10 stars in a dwarf galaxy to be 395.2 km/s. The standard deviation of the velocities is 30 km/s, and that is the best guess you have for the population standard deviation. What is the 99.7% confidence interval for your measurement?