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2 problems match “sample mean”. Clear

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1. Fitting b through sample means ●●○○○ 20 ptsA sample of six points $(x_1, y_1), \ldots, (x_6, y_6)$ is scattered around the curve $y = bx^2 - \frac{1}{3}$, where $b$ is a real number. Given $\sum_{i=1}^{6} x_i = 11$, $\sum_{i=1}^{6} y_i = 13$ and $\sum_{i=1}^{6} x_i^2 = 21$, find $b$ using the regression line in the variable $t = x^2$. Round to two decimal places.
2. Martian species height difference probability ●●●○○ 50 ptsSpecies 1 heights are normally distributed with mean 32 and variance 60. Species 2 heights are normally distributed with mean 22 and variance 70. A sample of 10 members of Species 1 and a sample of 14 members of Species 2 are drawn independently. Find the probability that the sample mean of Species 1 exceeds the sample mean of Species 2 by 5 or more. Round to three decimal places.