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coldgirl [10]
3 years ago
13

Teacher's salaries in Georgia are normally distributed with an average salary of $52,000 with a standard deviation of $12,000. W

hat percentage of teachers earn an a salary between $40,000 and $76,000?
Mathematics
1 answer:
suter [353]3 years ago
8 0

Answer:

81.85%

Step-by-step explanation:

We have the following information:

mean = m = 52000

standard deviation = sd = 12000

a = 40000

b = 76000

we need to find the probability between a and b, that is:

P (a <x <b) = P (40,000 <x <76000)

P [(40000 - m) / sd <(x - m) / sd <(76000 - m) / sd]

replacing

P [(40000 - 52000) / 12000 <z <(76000 - 52000) / 12000]

P (-1 <z <2)

P (z <= -1) - P (z <= 2)

We look for this value of z, in the attached table:

0.9772 - 0.1587

P = 0.8185

In other words, the probability is 81.85%

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In 1998, Cathy's age is equal to the sum of the four digits in the year of her birthday, then how old was Cathy in 1998?
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Answer:

<em>Cathy was born in 1980 and she was 18 years old in 1998</em>

Step-by-step explanation:

<u>Equations</u>

This is a special type of equations where all the unknowns must be integers and limited to a range [0,9] because they are the digits of a number.

Let's say Cathy was born in the year x formed by the ordered digits abcd. A number expressed by its digits can be calculated as

x=1000a+100b+10c+d

In 1998, Cathy's age was

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And it must be equal to the sum of the four digits

1998-(1000a+100b+10c+d)=a+b+c+d

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We are sure a=1, b=9 because Cathy's age is limited to having been born in the same century and millennium. Thus

1998=1001+909+11c+2d

Operating

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If now we try some values for c we notice there is only one possible valid combination, since c and d must be integers in the range [0,9]

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Thus, Cathy was born in 1980 and she was 18 years old in 1998. Note that 1+9+8+0=18

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3 years ago
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Answer:

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Step-by-step explanation:

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From the figure we can see a right angled triangle.

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To find the value of x

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