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Juli2301 [7.4K]
3 years ago
14

The equatorial radius of the planet Jupiter is measured 40 times by a process that is practically free of bias. These measuremen

ts average is 71492 kilometers with a standard deviation of 28 kilometers. Find a 93% confidence interval for the equatorial radius of Jupiter
Mathematics
1 answer:
Nina [5.8K]3 years ago
8 0

Answer:

The 93% confidence interval for the equatorial radius of Jupiter is between 71484 km and 71500 km.

Step-by-step explanation:

Sample size of 30 or larger, so we can use the normal distribution to find the confidence interval.

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.93}{2} = 0.035

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.035 = 0.965, so z = 1.81

Now, find M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 1.81*\frac{28}{\sqrt{40}} = 8

The lower end of the interval is the sample mean subtracted by M. So it is 71492 - 8 = 71484 km.

The upper end of the interval is the sample mean added to M. So it is 71492 + 8 = 71500 km.

The 93% confidence interval for the equatorial radius of Jupiter is between 71484 km and 71500 km.

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