Math  /  Data & Statistics

Question28. An engineer wants to find out whether to pave a particular section of road. To help with the decision, he finds out how many cars use the road each day. For 35 consecutive days, the number of cars is counted daily.A. Create 10 intervals and tally the raw data and fill in the missing values of the frequency chart. (5 marks)892912894879809926804908918913814872903893899879892907869874903898928859914902895938864884877880814803912IntervalTallyFrequency803816817830831844845858859872873886887900901914915928B. What percentage of days are there less than 900 cars on the road? Round your answer to the nearest percentage. (2 marks)\begin{array}{l} \text{28. An engineer wants to find out whether to pave a particular section of road. To help with the decision, he finds out how many cars use the road each day. For 35 consecutive days, the number of cars is counted daily.} \\ \text{A. Create 10 intervals and tally the raw data and fill in the missing values of the frequency chart. (5 marks)} \\ \begin{array}{llllllllllll} 892 & 912 & 894 & 879 & 809 & 926 & 804 & 908 & 918 & 913 & 814 & 872 \\ 903 & 893 & 899 & 879 & 892 & 907 & 869 & 874 & 903 & 898 & 928 & 859 \\ 914 & 902 & 895 & 938 & 864 & 884 & 877 & 880 & 814 & 803 & 912 & \\ \end{array} \\ \hline \\ \begin{array}{|c|c|c|} \hline \text{Interval} & \text{Tally} & \text{Frequency} \\ \hline 803-816 & & \\ \hline 817-830 & & \\ \hline 831-844 & & \\ \hline 845-858 & & \\ \hline 859-872 & & \\ \hline 873-886 & & \\ \hline 887-900 & & \\ \hline 901-914 & & \\ \hline 915-928 & & \\ \hline \end{array} \\ \text{B. What percentage of days are there less than 900 cars on the road? Round your answer to the nearest percentage. (2 marks)} \\ \end{array}

Studdy Solution

STEP 1

What is this asking? We need to organize car counts into groups, figure out how many days fall into each group, and then calculate the percentage of days with fewer than 900 cars. Watch out! Don't forget to include the endpoints of the intervals when counting, and make sure to round the final percentage correctly!

STEP 2

1. Tally and Count
2. Calculate the Percentage

STEP 3

Let's **organize** our car count data into the given intervals.
This makes it easier to see how many days fall into each group.

STEP 4

For the interval 803-816, we have: 809, 804, 814, 814, 803.
That's **5** days!
Tally: |||||.

STEP 5

No data falls into this interval. **Frequency: 0**.
Tally:

STEP 6

No data falls into this interval. **Frequency: 0**.
Tally:

STEP 7

No data falls into this interval. **Frequency: 0**.
Tally:

STEP 8

We have 859, 872.
That's **2** days!
Tally: ||.

STEP 9

We have 879, 869, 874, 864, 877, 879, 884, 880.
That's **8** days!
Tally: ||||||||.

STEP 10

We have 892, 894, 893, 899, 892, 895, 898.
That's **7** days!
Tally: |||||||.

STEP 11

We have 912, 908, 913, 903, 907, 903, 902, 914, 912.
That's **9** days!
Tally: ||||||||||.

STEP 12

We have 926, 918, 928.
That's **3** days!
Tally: |||.

STEP 13

We need to find the number of days with less than 900 cars.
This includes all the intervals *before* 901-914.
Adding up the frequencies from those intervals: 5+0+0+0+2+8+7=225 + 0 + 0 + 0 + 2 + 8 + 7 = 22.
So, there are **22** days with less than 900 cars.

STEP 14

We know the engineer counted cars for **35** consecutive days.

STEP 15

To find the percentage, we divide the number of days with less than 900 cars (**22**) by the total number of days (**35**) and multiply by 100: 223510062.86 \frac{22}{35} \cdot 100 \approx 62.86 Rounding to the nearest percentage gives us **63%**.

STEP 16

On approximately **63%** of the days, there were less than 900 cars on the road.

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