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Step2247 [10]
3 years ago
11

IQ tests are scaled so that the mean score in a largepopulation should be μ =100. We suspect that the very-low-birth-weight popu

lation has mean score less than100. Infants weiging less than 1500 grams at birth are classed as "very low birth weight". Low birth weight carriesmany risks. One study followed 113 male infants with very low birth weight to adulthood. At age 20, the mean IQ score for these men was (x bar=87.6.) Iq scores vary Normally with standard deviation σ=15. Give a 95% confidence interval for the mean IQ score at age 20 for allvery-low-birth-weight males. Use the four-step process for confidence interval.
Mathematics
1 answer:
Rudiy273 years ago
5 0

Answer:

The 95% confidence interval is  84.83<  \mu < 90.37

Step-by-step explanation:

From the question we are told that

    The  sample size is  n  = 113

     The sample mean is  \= x  =  87.6  

      The standard deviation is  \sigma  =  15

     

Given that the confidence level is  95% then the level of significance is mathematically represented as

            \alpha  =  100 - 95

             \alpha  =  5\%

             \alpha  =  0.05

Next we obtain the critical value of  \frac{\alpha }{2} from the normal distribution table, the value  is  

              Z_{\frac{ \alpha }{2} } =  1.96

Generally the margin of error is mathematically evaluated as

              E =  Z_{\frac{\alpha }{2} } *  \frac{ \sigma}{ \sqrt{n} }

=>          E =  1.96  *  \frac{ 15}{ \sqrt{113} }

=>          E =  2.77

The  95% confidence interval is mathematically represented as

          \= x - E <  \mu <   \= x + E

substituting values

        87.6  - 2.77<  \mu < 87.6  + 2.77

        84.83<  \mu < 90.37

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alexdok [17]

Answer:

m<R=44.9,m<S=56.9,m<T=44.9,m<U= 32.9.

Step-by-step explanation:

When two chords are equal then the measure of the arcs are equal.

Chord RU= Chord UT

Or , m arc RU= m arc UT,

3z-4=x+2z+7   Or             z=x+11

Chord RS=Chord ST ,

m arc RS=m arc ST=3x+5

Sum of m arc in a circle =360 degrees.

Or ,

3x+5+3x+5+3z-4+x+2z+7=360

7x+5z+13=360

Substituting z=x+11

7x+5(x+11)+13=360

7x+5x+55+13=360

12x+68=360

12x=292,x=24.3

z=x+11=11+24.3=34.3

m arc RU=marc UT= 3z-4=3(24.3)-4=69

m arc RS =marc ST= 3x+5=3(24..3)+5=77.9

m<R= (marc UT+ m  arc ST)÷2

m<R=(69+77.9)÷2=73.45

m<S= (m arc RU+m arc UT)÷2

m<S= (69+69)÷2=69

m<T=(m arc RU+m arc RS)÷2=73.45

m<U=(m arc RS+m arc m arc ST)÷2=77.9








4 0
3 years ago
Please help Im in class
atroni [7]

Answer:

sorry cant help

Step-by-step explanation:

7 0
3 years ago
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During a catered lunch, an average of 4 cups of tea are poured per minute. The lunch will last 2 hours. How many gallons of tea
Greeley [361]

Answer:

Step-by-step explanation:

4 cups of tea per minute.......lunch lasts 2 hrs.....there are 120 minutes in 2 hrs...so in 2 hrs, there will be (4 * 120) = 480 cups

and if there is 16 cups in 1 gallon, the caterer needs to bring :

480 / 16 = 30 gallons <==

6 0
3 years ago
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There are 12 boys and 15 girls in your class for new students three boys and one girl join your class what is the ratio of the c
Finger [1]
Before the new kids the ratio of girls to boys is 15:12 because there are 15 girls and 12 boys now you can simplify by dividing 15 by 3 and 12 by 3 to get 5:4 as your simplified ratio. As far as after the new kids. Since there is 1 new girl you do 15+1 to get 16 and there are 3 new boys so you do 12+3 to get 15 now 16:15 is already in simplest form so your answer is:

Before: 15:12 simplified as 5:4
After 16:15
6 0
2 years ago
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Expand 2(q+3) please
Y_Kistochka [10]

Answer:

  • 2q + 6

Step-by-step explanation:

<u>Expand the expression with the help of distributive property.</u>

  • 2(q + 3)
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  • => 2q + 6

Hence, the expanded expression is 2q + 6.

5 0
2 years ago
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