A population of values has a normal distribution with $\mu = 164.7$ and $\sigma = 38.9$. You intend to draw a random sample of size $n = 71$. Find the probability that a single randomly selected value is between 149.9 and 167. $P(149.9 < X < 167) =$ Find the probability that a sample of size $n = 71$ is randomly selected with a mean between 149.9 and 167. $P(149.9 < M < 167) =$
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9 and 167. We can use the normal distribution with $\mu = 164.7$ and $\sigma = 38.9$. First, we calculate the z-scores for 149.9 and 167: $z_1 = \frac{149.9 - 164.7}{38.9} = \frac{-14.8}{38.9} \approx -0.3805$ $z_2 = \frac{167 - 164.7}{38.9} = \frac{2.3}{38.9} Show more…
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