Mathematics, 14.06.2020 03:57 lbelle

Problem 3 Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 300 feet and a standard deviation of 50 feet. Let X= distance in feet for a fly ball. In each appropriate box you are to enter either a rational number in "p/q" format or a decimal value accurate to the nearest 0.01 . X∼ ( 300 , 50 ) . For a random fly ball, what is the probability that this ball traveled fewer than 220 feet? P(X<220)= 0.05 . The 80th percentile of the distribution of fly balls is given by P(X< 342 )=0.80 .

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Answer from: damariush567

P(X < 220) = 0.05

The 80th percentile of the distribution of fly balls is 342 feet.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 300, \sigma = 50$

P(X<220)

This is the pvalue of Z when X = 220. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{220 - 300}{50}$

Z = -1.6

Z = -1.6 has a pvalue of 0.0548

Rounding to two decimal places

P(X < 220) = 0.05

80th percentile:

X when Z has a pvalue of 0.8. So X when Z = 0.84. So

$Z = \frac{X - \mu}{\sigma}$

$0.84 = \frac{X - 300}{50}$

X - 300 = 50*0.84

X = 342

The 80th percentile of the distribution of fly balls is 342 feet.

Answer from: Quest

answer set (b) 0.5, 3/4 80% is in order from least to greatest.

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form. typically, the best form in which to evaluate rational numbers is in decimals. in order to convert a percent to a decimal, you would divide the given percentage by 100. you can also accomplish the conversion by moving the decimal point over two places to the left. for example, the decimal value of 80% is 80/100, or 0.8. in order to convert a fraction to a decimal, you need to divide the numerator by the denominator. for example, 3/4 is 0.75. so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.

Answer from: Quest

3,750 deer

step-by-step explanation:

1,500 is 15 times larger than 100

lets make 250 15 times larger.

3750 deer