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lozanna [386]
2 years ago
11

The table gives information about the speeds, in kilometres per hour, of 80 motorbikes as each pass under a bridge.

Mathematics
1 answer:
natka813 [3]2 years ago
6 0

The modal class is 70 - 80 and the mean speed is 66.4

<h3>How to determine the modal class?</h3>

The table of values is given as:

Speed    Frequency

40 - 50          10

50 - 60          16

60 - 70          19

70 - 80          23

80 - 90          12

The modal class is the class with the highest frequency

The class 70 - 80 has the highest frequency of 23

Hence, the modal class is 70 - 80

<h3>How to determine the mean?</h3>

Rewrite the frequency table to include the class midpoints

x             f

45          10

55          16

65          19

75          23

85          12

The estimate of the mean speed is then calculated as:

\bar x =\frac{\sum fx}{\sum f}

So, we have:

\bar x = \frac{45* 10 +  55 * 16 + 65 * 19 + 75 * 23 + 85 * 12}{80}

Evaluate

\bar x = 66.4

Hence, the mean speed is 66.4

Read more about mean and mode at:

brainly.com/question/14532771

#SPJ1

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Answer:

a) P [ X < 24 mm ] = 0,3015          or     P [ X < 24 mm ] =  30,15 %

b) P [ X > 32 mm ]  = 0,1251          or        P [ X > 32 mm ]  = 12,51 %

c) P [  25 < X < 30 ] = 0,4964      or     P [  25 < X < 30 ] = 49,64 %

d) z(s) = 0,84

Step-by-step explanation:

Normal Distribution    N (  μ₀  ;   σ )   is  N ( 26,5 ; 4,8 )

a) P [ X < 24 mm ] = ( X - μ₀ ) / σ

P [ X < 24 mm ] = (24 - 26,5)/ 4,8 = - 0,5208 ≈ - 0,52

P [ X < 24 mm ] = - 0,52  

And from z-table we find area for z score

P [ X < 24 mm ] = 0,3015          or     P [ X < 24 mm ] =  30,15 %

b)P [ X > 32 mm ]  =  1  - P [ X < 32 mm ]

P [ X < 32 mm ]  = ( 32 - 26,5 ) / 4,8

P [ X < 32 mm ]  = 5,5/4,8  =  1,1458 ≈ 1,15

P [ X < 32 mm ]  = 1,15

And from z-table  we get

P [ X < 32 mm ]  = 0,8749

Then:

P [ X > 32 mm ]  =  1  -  0,8749

P [ X > 32 mm ]  = 0,1251          or        P [ X > 32 mm ]  = 12,51 %

c) P [  25 < X < 30 ] = P [ X < 30 ] - P [ X < 25 ]

P [ X < 30 ]  = 30 - 26,5 / 4,8   =  0,73

From  z-table    P [ X < 30 ]  =  0,7673

P [ X < 25 ] = 25 - 26,5 / 4,8  = - 0,3125  ≈  - 0,31

From z-table  P [ X < 25 ] =  0,2709

Then

P [  25 < X < 30 ] =  0,7673 -  0,2709

P [  25 < X < 30 ] = 0,4964      or     P [  25 < X < 30 ] = 49,64 %

d) If  20 %

z- score for 20% is from z-table

z(s) = 0,84

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Answer:

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1 - 7/8 of the box of cereal which is 1/8.

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