If 270 people chose math as their favorite subject, how many people were surveyed?

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

2 years ago

Can someone help me understand how to do this ?

Damm [24]

Do you know your trig ratios?

3 0

3 years ago

Liam is saving up to buy a new pair of Jordan's that cost

Andreyy89

Answer:

9 weeks

Step-by-step explanation:

5 0

3 years ago

Find the exact values of all three trigonometric functions for each angle.

My name is Ann [436]

Answer:

Sin (270º)= -1

Cos (270º) = 0

Tan (270º) = -∞

Sin (330º) = -0.5

Cos (330º) = $\frac{\sqrt{3} }{2}$ = 0.8660

Tan (330º) = - $\frac{\sqrt{3} }{3} \\$ = -0.57735

Step-by-step explanation:

3 0

3 years ago

On the next test, one of the students score 100 but the remaining 4 students score 50 again. What is the average score on this s

Anastasy [175]

Answer:

60

Step-by-step explanation:

50+50+50+50+100= 300

divide by 5 students

300/5 = 60

7 0

2 years ago

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