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bulgar [2K]
3 years ago
11

The weights of tennis balls are normally distributed, with the mean being 5.15 ounces and the standard deviation being 0.10. wha

t percentage of the balls weigh within one standard deviation of the mean? 50% 68% 95% 99.7%
Mathematics
1 answer:
zlopas [31]3 years ago
8 0
The empirical rule for normal distributions states that approximately 68% of the data points lie within the range plus and minus one standard deviation of the mean.
The answer is 68%.
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Customers arrive at a service facility according to a Poisson process of rate λ customers/hour. Let X(t) be the number of custom
mash [69]

Answer:

Step-by-step explanation:

Given that:

X(t) = be the number of customers that have arrived up to time t.

W_1,W_2... = the successive arrival times of the customers.

(a)

Then; we can Determine the conditional mean E[W1|X(t)=2] as follows;

E(W_!|X(t)=2) = \int\limits^t_0 {X} ( \dfrac{d}{dx}P(X(s) \geq 1 |X(t) =2))

= 1- P (X(s) \leq 0|X(t) = 2) \\ \\ = 1 - \dfrac{P(X(s) \leq 0 , X(t) =2) }{P(X(t) =2)}

=  1 - \dfrac{P(X(s) \leq 0 , 1 \leq X(t)) - X(s) \leq 5 ) }{P(X(t) = 2)}

=  1 - \dfrac{P(X(s) \leq 0 ,P((3 \eq X(t)) - X(s) \leq 5 ) }{P(X(t) = 2)}

Now P(X(s) \leq 0) = P(X(s) = 0)

(b)  We can Determine the conditional mean E[W3|X(t)=5] as follows;

E(W_1|X(t) =2 ) = \int\limits^t_0 X (\dfrac{d}{dx}P(X(s) \geq 3 |X(t) =5 )) \\ \\  = 1- P (X(s) \leq 2 | X (t) = 5 )  \\ \\ = 1 - \dfrac{P (X(s) \leq 2, X(t) = 5 }{P(X(t) = 5)} \\ \\ = 1 - \dfrac{P (X(s) \LEQ 2, 3 (t) - X(s) \leq 5 )}{P(X(t) = 2)}

Now; P (X(s) \leq 2 ) = P(X(s) = 0 ) + P(X(s) = 1) + P(X(s) = 2)

(c) Determine the conditional probability density function for W2, given that X(t)=5.

So ; the conditional probability density function of W_2 given that  X(t)=5 is:

f_{W_2|X(t)=5}}= (W_2|X(t) = 5) \\ \\ =\dfrac{d}{ds}P(W_2 \leq s | X(t) =5 )  \\ \\  = \dfrac{d}{ds}P(X(s) \geq 2 | X(t) = 5)

7 0
4 years ago
What percent of 120 is 20?
Aneli [31]

Answer:

16.67

Step-by-step explanation:

Step 1: We make the assumption that 20 is 100% since it is our output value.

Step 2: We next represent the value we seek with x.

Step 3: From step 1, it follows that 100%=20.

Step 4: In the same vein.

Step 5: This gives us a pair of simple equations

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS

Step 7: Taking the inverse (or reciprocal) of both sides yields

6 0
3 years ago
Read 2 more answers
Jay just graduated from college and he has decided to open a retirement account that pays 1.75% interest compounded monthly. If
gayaneshka [121]

Answer:

50989.68

Step-by-step explanation:

add 100 to 1.75% then multiply by 12 then multiply by 42

hope that helps :)

4 0
3 years ago
Read 2 more answers
3 square root of negative 125
Leni [432]
The answer is 33.5410197i
6 0
3 years ago
Pamela and her friend Nicole are each baking apple pies and tarts for a bake sale, using the same recipes. Pamela baked 5 apple
valentina_108 [34]

Answer:

Each apple pie requires 8 apples, and each apple tart requires 4 apples.

Step-by-step explanation:

We see that both Pamela and Nicole bake the same amount of apple pies, but different amounts of apple tarts. Because of this, we can subtract the two to try to figure out the amount of apples for each apple tart. We subtract 68 from 76, giving us 8. Nicole baked 9 apple tarts, while Pamela baked 7, and 9-7=2. So we can bake two apple tarts with 8 apples, so one apple tart requires 4 apples (we divide by 2). Now that we know the amount of apples per each apple tart, we multiply 7 apple tarts that Pamela made by 4 apples, giving us 28. We subtract that from the total amount of apples Pamela used, which was 68, giving us 40. From this we can deduct that 5 apple pies need 40 apples, and we divide by 5, giving us 1 apple pie requires 8 apples.

3 0
3 years ago
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