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4 years ago

6

Guilia runs an average of 15 minutes each day.She has a goal of running 10 to the power of two minutes in 7 days. Will she compl

ete her running goal in 7 days?

1 answer:

zheka24 [161]4 years ago

6 0

Yes because 10 to the power of 2 is 100 and if she runs 15 minutes a day for 7 days that would = 105 minutes

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$0.45 - 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.287$

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Step-by-step explanation:

The estimated proportion of interest is $\hat p=0.45$

We need to find a critical value for the confidence interval using the normla standard distributon. For this case we have 95% of confidence, then the significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value is:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the true population proportion is interest is given by this formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

Replacing the values provided we got:

$0.45 - 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.287$

$0.45 + 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.613$

And we can conclude at 95% of confidence that the true proportion of interest for this case is between 0.287 and 0.613

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