Question

Enter numerical values as fractions in "p/q" format, or as decimals accurate to 0.01. Intermediate calculations need to be accurate to 0.001 to ensure that the final answers are accurate to 0.01 Problem 1 Suppose that the distance o feet. Let X distance in feet for a fly ball. of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 350 feet and a standard deviation of 60 In each appropriate box you are to enter either a rational number in p/q format or a decimal value accurate to the nearest 0. (3%) x ~ |(pick one) fly ball what is the probability that this ball traveled fewer than 220 feet? P(x <220)- P(X < q )-080 (3%) The 80th percentile of the distribution of fly balls is given by c. Problem 2

Answer 1

$\mathbf{SOLUTION}$

$\mathbf{given:}\;\mu=350,\;\sigma=60$

$formula:\;Z=\frac{X-\mu}{\sigma}$

$\mathbf{{\color{Blue} a.}}\;X\sim N(\mu,\sigma^{2})$

$X\sim N(350,\;60^{2})$

$X\sim \mathbf{{\color{Red} N(350,\;3600)}}$

-------------------------------------------------------------------------------------

$\mathbf{{\color{Blue} b.}}\;P(X<220)$

$=P\left (\frac{X-\mu}{\sigma} <\frac{220-350}{60} \right )$

$=P\left (Z<-2.17\right )$

$=\mathbf{0.0150}\;(from\;z-table)$

$\approx \mathbf{{\color{Red} 0.02}}$

-------------------------------------------------------------------------------------

$\mathbf{{\color{Blue} c.}}\;P(Z<?)=0.80$

from Z-table, lookup for z-value corresponding to area 0.80 to the left of the normal curve

$P(Z<0.84)=0.80$

$0.84=\frac{X-350}{60}$

$X=350&plus;(0.84*60)$

$X={\color{Red} \mathbf{400.40}}$

$P(X<\mathbf{{\color{Red} 400.40}})=0.80$