A baseball is hit inside a baseball diamond with a length and width of 90 feet each. What is the probability that the ball will bounce on the pitchers mound, if the diameter of the mound is 18 feet? Assume that the ball is equally likely to bounce anywhere in the infield. When applicable, leave your answer in terms of pie and include all necessary calculations.

Answers

Answer 1

Answer:

Answer:

$(\pi )/(100)$

Step-by-step explanation:

The first thing to notice is that the diamond is just a square rotated 45 degrees square, with 90 feet sides, so the total area of the diamond is:

A(square)= l x l = 90 ft * 90 ft = 8100 $ft^(2)$

We also need to calculate the area of the mound, assuming it being a circle:

A(circle)= $\pi * r^(2)$ And r=diameter/2= 18 ft/2 = 9 ft

A(circle) = $\pi * (9 ft)^(2)$ = 81 $\pi ft^(2)$

Now since the ball has an equal chance of bouncing anywhere in the field, the probability would be the ratio of the area occupied by the mound inside of the diamond.

P= $(81\pi ft^(2))/(8100 ft^(2))$ = $(\pi )/(100)$

Answer 2

Answer: 90(squared) + 90 (squared) = C (squared)
(we use 90 because the base path is 90 ft long since the diamond is a square that makes all sides 90 ft long)
8100 + 8100 = c(squared)
16200 = c(squared)
we will get the square root of 16200 to get the diagonal length
C=127.3 ft, and since it is the diagonal distance we will device it to 2, to get the distance from the pitcher ro the 2nd base.
127.3/2 = 67.7 ft.
67.7 ft is the distance from the pitcher to the 2nd base.

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2,4000,000 in standard form
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You have a litre bottle of water and drink 375 millilitres. How much is left?
Which expression is equivalent to the given expression?12(x – 17) A. 12x – 29 B. 12 + 12 • 17 C. 12x – 12 • 17 D. 12x – 17

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Answers

Answer:

-690/1000

Step-by-step explanation:

The answer is negative 690/1000

The blood platelet counts of a group of women have a bell-shaped distribution with a mean of and a standard deviation of . (All units are 1000 cells/L.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within standard of the mean, or between and ?
b. What is the approximate percentage of women with platelet counts between and ?

Answers

Answer:

(a) Approximately 95% of women with platelet counts within 2 standard deviations of the mean.

(b) Approximately 99.7% of women have platelet counts between 65.2 and 431.8.

Step-by-step explanation:

The complete question is: The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 248.5 and a standard deviation of 61.1. (All units are 1000 cells/mul.) using the empirical rule, find each approximate percentage below.

a. What is the approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 126.3 and 370.7?

b. What is the approximate percentage of women with platelet counts between 65.2 and 431.8?

We are given that the blood platelet counts of a group of women have a bell-shaped distribution with a mean of 248.5 and a standard deviation of 61.1.

Let X = the blood platelet counts of a group of women

The z-score probability distribution for the normal distribution is given by;

Z = $(X-\mu)/(\sigma)$ ~ N(0,1)

where, $\mu$ = population mean = 248.5

$\sigma$ = standard deviation = 61.1

Now, the empirical rule states that;

68% of the data values lie within 1 standard deviation away from the mean.

95% of the data values lie within 2 standard deviations away from the mean.

99.7% of the data values lie within 3 standard deviations away from the mean.

(a) The approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 126.3 and 370.7 is given by;

As we know that;

P( $\mu-2\sigma$ < X < $\mu+2\sigma$ ) = 0.95

P(248.5 - 2(61.1) < X < 248.5 + 2(61.1)) = 0.95

P(126.3 < X < 370.7) = 0.95

Hence, approximately 95% of women with platelet counts within 2 standard deviations of the mean.

(b) The approximate percentage of women with platelet counts between 65.2 and 431.8 is given by;

Firstly, we will calculate the z-scores for both the counts;

z-score for 65.2 = $(X-\mu)/(\sigma)$

= $(65.2-248.5)/(61.1)$ = -3

z-score for 431.8 = $(X-\mu)/(\sigma)$

= $(431.8-248.5)/(61.1)$ = 3

This means that approximately 99.7% of women have platelet counts between 65.2 and 431.8.

Final answer:

Using the empirical rule, approximately 68% of values fall within 1 standard deviation from the mean in a bell-shaped distribution. For ranges 2 or 3 standard deviations from the mean, the respective approximate percentages are 95% and 99.7%.

Explanation:

The question refers to the Empirical rule, which in statistics, is also known as the Three-sigma rule or the 68-95-99.7 rule. This rule is a shortcut for remembering the proportion of values in a normal distribution that are within a given distance from the mean: 68% are within 1 standard deviation, 95% are within 2 standard deviations, and 99.7% are within 3 standard deviations.

Without given specific values for the mean or standard deviations, we can discuss the problem in a general sense:

For part a, the percentage of women with platelet counts within 1 standard deviation from the mean is approximately 68% under the Empirical rule.
For part b, it depends on how many standard deviations from the mean the range mentioned lies. If it refers to two standard deviations from the mean, then 95% of women would fall into this range, if it refers to three standard deviations, then approximately 99.7% would be the case.