Including Jose, there are eight people in his family.

This question is poorly phrased

Complete Question

The lifespans of lions at a specific zoo follow a normal distribution. The average lifespan is 12.5 years with a standard deviation of 2.4 years. Apply the empirical rule (68-95-99.7%) to estimate the likelihood of a lion living between 5.3 and 10.1 years.

Answer:

The likelihood of a lion living from 5.3 to 10.1 years is 0.1585

Step-by-step explanation:

According to the empirical rule:

1) 68% of the data falls within 1 standard deviation of the mean, meaning between μ - σ and μ + σ.

2) 95% of the data is contained within 2 standard deviations around the mean - between μ - 2σ and μ + 2σ.

3) 99.7% of the data lies within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

The mean provided is: 12.5

Standard deviation: 2.4 years

Starting with the first rule:

1) 68% falls within 1 standard deviation from the mean, implying between μ - σ and μ + σ.

μ - σ

12.5 - 2.4

= 10.1

We now apply the second rule:

2) 95% of the data lies within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.

μ – 2σ

12.5 - 2 × 2.4

12.5 - 4.8

= 7.7

Now applying the last rule:

3)99.7% of the data resides within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

μ - 3σ

= 12.5 - 3(2.4)

= 12.5 - 7.2

= 5.3

The calculations indicate that

5.3 years is at one side of 99.7%

Therefore,

100 - 99.7%/2 = 0.3%/2

= 0.15%

Moreover, 10.1 years corresponds to one side of 68%

Thus

100 - 68%/2 = 32%/2 = 16%

Consequently, the percentage of a lion living between 5.3 to 10.1 years is evaluated as 16% - 0.15%

= 15.85%

Thus, the estimated probability of a lion surviving between 5.3 and 10.1 years

is represented as a decimal =

= 15.85/ 100

= 0.1585

Let's convert each statement into mathematical terms.

Pineapple = p

Orange = x

is indicates equality

 

Pineapple has a weight that is 7 times that of an orange:  p = 7x

Pineapple is 870 grams heavier than the orange. p = 870 + x

 

Insert  p = 7x  into the second equation:

7x = 870 + x

Subtract  x from both sides

6x = 870

Divide by 6

x = 145

 

The weight of the orange is 145 grams.

The weight of the pineapple is 7 times that of the orange = 7(145) = 1015 grams.

Nearest hundred thousand: 100,000

Nearest ten thousand: 130,000

Nearest thousand: 127,000

The amount that is closest to the actual attendance is 127,000 when rounded to the nearest thousand.

Zx = 5g(2x - c) Apply the Distributive Property
zx = 10gx - 5cg Subtract 10gx from each side
zx - 10gx = -5cg Factor x out
x (z - 10g) = -5cg Divide by (z - 10g)
x =

Answer:

Kathy: $1,224,000

Mark: $306,000

Please refer to the attachment.