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fgiga [73]
3 years ago
14

A group of 59 randomly selected students have a mean score of 29.5 with a standard deviation of 5.2 on a placement test. What is

the​ 90% confidence interval for the mean​ score, muμ​, of all students taking the​ test?
Mathematics
1 answer:
BigorU [14]3 years ago
4 0

Answer:

29.5+/-1.11

= ( 28.39, 30.61)

Therefore, the 90% confidence interval (a,b) =( 28.39, 30.61)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = 29.5

Standard deviation r = 5.2

Number of samples n = 59

Confidence interval = 90%

z-value (at 90% confidence) = 1.645

Substituting the values we have;

29.5+/-1.645(5.2/√59)

29.5+/-1.645(0.676982337100)

29.5+/-1.113635944529

29.5+/-1.11

= ( 28.39, 30.61)

Therefore, the 90% confidence interval (a,b) =( 28.39, 30.61)

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Kimberly has 20.95 in her purse. She buys lunch for $9.67. How much does she have left?
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Kimberly has $11.28 left

Step-by-step explanation:

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Which of the following ordered pairs represents a solution to the linear inequality y<6x-4? A. (0,3) B.(0,11) C. (0,-5) D.(0,
son4ous [18]

Answer:

<u>Option C. (0,-5)</u>

Step-by-step explanation:

See the attached figure.

As shown the shaded area represents the solution of the given inequality:

y < 6x - 4

The given options are the points:

A. (0,3) B.(0,11) C. (0,-5) D.(0,4)

Comparing the given points to the graph.

So, the point that will lie at the shaded area represent  solution to the linear inequality.

So, point (0,-5) is a solution to the linear inequality.

The answer is <u>option C. (0,-5)</u>

Note: the line y = 6x-4 is graphed using the table on the graph.

4 0
3 years ago
The Los Angeles Times regularly reports the air quality index for various areas of Southern California. A sample of air quality
egoroff_w [7]

Answer:

1. (a) 32     (b) 8

2. (a) 48.33    (b) 92.75    (c) 9.63

3.  We observe that sample mean of air quality index in Pomona is higher that that of Anaheim which indicates that the level of air pollution is higher in Pomona and there is more health concern here.

On the other hand, the variation in air quality index is higher in Anaheim than in Pomona as Anaheim has higher variance and standard deviation for air quality index which means that there are not much fluctuations in air quality index in Pomona.  

Step-by-step explanation:

First arranging our data of air quality index values for Pomona in ascending order, we get : 28, 42, 45, 48, 49, 50, 55, 58, 60.

  1. (a) Range is given by the formula :

                      Highest value in data - Lowest value in data = 60 - 28 = 32

        (b) Interquartile rage = Third quartile - First quartile

                                           = Q_3 - Q_1

             Q_1 =  (\frac{n-1}{4} )^{th} observation in the data = 2^{nd} obs. { Because n = 9}

                 Therefore, Q_1 = 42.

             Q_3 = (3Q_1)^{th} obs. = (3 x 2 ) = 6^{th} obs = 50

             So, Interquartile rage = 50 - 42 = 8.

     2. (a) Sample mean formula =  \frac{\sum X_i}{n} = \frac{28+ 42+ 45+ 48+ 49+ 50+ 55+ 58+ 60}{9} = 48.33

         (b) Sample variance formula = \frac{\sum (X_i - Xbar)^{2}}{n-1} where Xbar = Sample mean

                                                         = 92.75

          (c) Sample standard deviation  formula = \sqrt{variance} = \sqrt{92.75} = 9.63.

     3. Given that a sample of air quality index readings for Anaheim has   sample mean of 48.3, a sample variance of 136, and a sample standard deviation of 11.66.

We observe that sample mean of air quality index in Pomona is higher that that of Anaheim which indicates that the level of air pollution is higher in Pomona and there is more health concern here.

On the other hand, the variation in air quality index is higher in Anaheim than in Pomona as Anaheim has higher variance and standard deviation for air quality index which means that there are not much fluctuations in air quality index in Pomona.  

                                       

7 0
2 years ago
Amy needs to mail a gift card to a friend. She uses 47-cent stamps and 6-cent stamps to pay $2.42 in postage. How many of each s
AVprozaik [17]

Answer:

Answer:Amy used 4 41-cent stamps and 8 6-cent stamps.

Step-by-step explanation:

Let x represent the number of 41-cent stamps that Amy used. Let y represent the number of 6-cent stamps that Amy used.

41 cents = 41/100 = $0.41

6 cents = 6/100 = $0.06

She uses 41-cent stamps and 6-cent stamps to pay $2.12 in postage. It means that

0.41x + 0.06y = 2.12

Multiplying through by 100, it becomes

41x + 6y = 212

6y = 212 -41x

We would test for corresponding values of x and y that satisfies the equation and they must be whole numbers.

If x = 3,

6y = 212 - 41 × 3 = 89

y = 89/6 = 14.8333

If x = 4,

6y = 212 - 41 × 4 = 48

y = 48/6 = 8

Answer:Amy used 4 41-cent stamps and 8 6-cent stamps.

Step-by-step explanation:

Let x represent the number of 41-cent stamps that Amy used. Let y represent the number of 6-cent stamps that Amy used.

41 cents = 41/100 = $0.41

6 cents = 6/100 = $0.06

She uses 41-cent stamps and 6-cent stamps to pay $2.12 in postage. It means that

0.41x + 0.06y = 2.12

Multiplying through by 100, it becomes

41x + 6y = 212

6y = 212 -41x

We would test for corresponding values of x and y that satisfies the equation and they must be whole numbers.

If x = 3,

6y = 212 - 41 × 3 = 89

y = 89/6 = 14.8333

If x = 4,

6y = 212 - 41 × 4 = 48

y = 48/6 = 8

8 0
2 years ago
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