Evaluate 20/y - 8/x + 3xy/x+y when x=2 and y=5

A random sample of 36 students at a community college showed an average age of 25 years. Assume the ages of all students at the

Pavel [41]

Answer:

98% confidence interval for the average age of all students is [24.302 , 25.698]

Step-by-step explanation:

We are given that a random sample of 36 students at a community college showed an average age of 25 years.

Also, assuming that the ages of all students at the college are normally distributed with a standard deviation of 1.8 years.

So, the pivotal quantity for 98% confidence interval for the average age is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample average age = 25 years

$\sigma$ = population standard deviation = 1.8 years

n = sample of students = 36

$\mu$ = population average age

So, 98% confidence interval for the average age, $\mu$ is ;

P(-2.3263 < N(0,1) < 2.3263) = 0.98

P(-2.3263 < $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ < 2.3263) = 0.98

P( $-2.3263 \times {\frac{\sigma}{\sqrt{n} }$ < ${\bar X - \mu}$ < $2.3263 \times {\frac{\sigma}{\sqrt{n} }$ ) = 0.98

P( $\bar X - 2.3263 \times {\frac{\sigma}{\sqrt{n} }$ < $\mu$ < $\bar X +2.3263 \times {\frac{\sigma}{\sqrt{n} }$ ) = 0.98

98% confidence interval for $\mu$ = [ $\bar X - 2.3263 \times {\frac{\sigma}{\sqrt{n} }$ , $\bar X +2.3263 \times {\frac{\sigma}{\sqrt{n} }$ ]

= [ $25 - 2.3263 \times {\frac{1.8}{\sqrt{36} }$ , $25 + 2.3263 \times {\frac{1.8}{\sqrt{36} }$ ]

= [24.302 , 25.698]

Therefore, 98% confidence interval for the average age of all students at this college is [24.302 , 25.698].

8 0

3 years ago

HELP WITH THIS ASAP!

Mars2501 [29]

Answer:

Hi, there your answer will C. 85pi ft^2

Step-by-step explanation:

pi(5)(12)+pi(5)^2

60pi+25pi

85pi ft^2

Hope this helps :)

8 0

3 years ago

if the radius of one of the semi-circles is 7 meters what is the circumference of one of the semi-circles

Yanka [14]

Answer: 43.96 m

Step-by-step explanation:

the circumference of one of the semi circle radius of one of the semicircles is 7 meters is 7 meters

ur welcome

3 0

3 years ago

You are given f(0) = 1 and g(0) = -2 and g(1) = 3. What is g ∘ f ( 0 ) equal to?

Sergeu [11.5K]

Answer:

g∘f (0) = 1

Explanation:

The composition of the functions f and g represented by g ∘ f ( 0 ) means that g is applied to f(0), i.e f(0) is the input to the function g.

Since f(0) = 1, you are going fo find g(1):

$$ g\circ f(x)=g(f(x)) $\\\\$ g\circ f(0)=g(f(0)) $\\\\$ g\circ f(0)=g(1) $=3$

4 0

3 years ago

You want to put some money in a simple interest account it pays 8% interest annually for 2 years you would like to earn 500 doll

Semmy [17]

You deposit some money into a bank account paying 8% simple interest per year. You received $500 in interest after 2 years. How much the deposit (principal) was?

Result

The principal was $3125.

Explanation

Find principal by using the formula I=P⋅i⋅t, where I is interest, P is total principal, i is rate of interest per year, and t is total time in years.

In this example I = $500, i = 8% and t = 2 years, so

IPPP=P⋅i⋅t=Ii⋅t=5000.08⋅2=3125

4 0

3 years ago

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