4x - 2y = 5 and y = 3x

The following table shows scores obtained in an examination by B.Ed JHS Specialism students. Use the information to answer the q

Makovka662 [10]

Answer:

(a) The cumulative frequency curve for the data is attached below.

(b) (i) The inter-quartile range is 10.08.

(b) (ii) The 70th percentile class scores is 0.

(b) (iii) the probability that a student scored at most 50 on the examination is 0.89.

Step-by-step explanation:

(a)

To make a cumulative frequency curve for the data first convert the class interval into continuous.

The cumulative frequencies are computed by summing the previous frequencies.

The cumulative frequency curve for the data is attached below.

(b)

(i)

The inter-quartile range is the difference between the third and the first quartile.

Compute the values of Q₁ and Q₃ as follows:

Q₁ is at the position:

$\frac{\sum f}{4}=\frac{100}{4}=25$

The class interval is: 34.5 - 39.5.

The formula of first quartile is:

$Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h$

Here,

l = lower limit of the class consisting value 25 = 34.5

(CF) $_{p}$ = cumulative frequency of the previous class = 24

f = frequency of the class interval = 20

h = width = 39.5 - 34.5 = 5

Then the value of first quartile is:

$Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h$

$=34.5+[\frac{25-24}{20}]\times5\\\\=34.5+0.25\\=34.75$

The value of first quartile is 34.75.

Q₃ is at the position:

$\frac{3\sum f}{4}=\frac{3\times100}{4}=75$

The class interval is: 44.5 - 49.5.

The formula of third quartile is:

$Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h$

Here,

l = lower limit of the class consisting value 75 = 44.5

(CF) $_{p}$ = cumulative frequency of the previous class = 74

f = frequency of the class interval = 15

h = width = 49.5 - 44.5 = 5

Then the value of third quartile is:

$Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h$

$=44.5+[\frac{75-74}{15}]\times5\\\\=44.5+0.33\\=44.83$

The value of third quartile is 44.83.

Then the inter-quartile range is:

$IQR = Q_{3}-Q_{1}$

$=44.83-34.75\\=10.08$

Thus, the inter-quartile range is 10.08.

(ii)

The maximum upper limit of the class intervals is 69.5.

That is the maximum percentile class score is 69.5th percentile.

So, the 70th percentile class scores is 0.

(iii)

Compute the probability that a student scored at most 50 on the examination as follows:

$P(\text{Score At most 50})=\frac{\text{Favorable number of cases}}{\text{Total number of cases}}$

$=\frac{10+4+10+20+30+15}{100}\\\\=\frac{89}{100}\\\\=0.89$

Thus, the probability that a student scored at most 50 on the examination is 0.89.

5 0

4 years ago

At this rate, how long will it take to sell 200 cups of coffee?<br> pls help me

Alja [10]

Answer: You didn't add a picture to help

Step-by-step explanation:

Once you do, I would be glad to edit my and help.

6 0

4 years ago

annie adds 2 spoonfuls of sugar to her tea and sophie adds 3 spoonfuls to her tea. If one spoonful is 4 grams of sugar and a a c

Tresset [83]

240%

Step-by-step explanation:

if there is 240 grams then you just put a percent sing but are you asking What is the percentage of sugar in each cup? by spoons?

3 0

3 years ago

Ten boys and twelve girls decide to rent a 16-passenger van and a 6-passenger to drive to a rock concert in a near by city. If t

stira [4]

A) The probability that there are no boys in the car is given by:
$P(no\ boys\ in\ car)=\frac{12C6}{22C6}=0.012$

5 0

3 years ago

A teacher is assessing the correlation between the number of hours spent studying and the average score on a music test. The tab

Bumek [7]

There is a correlation between the number of hours spent on studies and the score on music tests.

We have given that,

The table below shows the data:

Number of hours spent studying (x) 0 0.5 1 1.5 2 2.5 3 3.5 4

Score on music test (y) 60 62 64 66 68 70 72 74 76

<h3>How to explain the correlation?</h3>

As we increase the 0.5 hours of studying, then the music score increases by 2. The function which best fits the data for the correlation is y=60 + 4x

The slope and y-intercept of the plot indicate that Y= score obtained in music test and number of hours spent on studying.

The slope of the above equation represents the rate of increase in music score with respect to an increase in the number of hours spent on studying.

The y-intercept gives the music score when the number of hours spent on studying is zero.

Learn more about correlation on:

brainly.com/question/4219149

#SPJ1

4 0

2 years ago

4x - 2y = 5 and y = 3x - 1