How do I interpret this question to get the data out? How do I set up the equations for the probability section?

Question

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Concrete strength is usually related to its strength at 28 days based on the load that a standard cube of concrete can sustain when tested in compression in a compression testing rig. The data below contains the results for a series of 40 concrete strength tests undertaken on a construction project currently being developed by your company.

Data	Data
Cube No.	fc (N/mm2)	Cube No.	fc (N/mm2)
1	36.64	21	23.47
2	40.96	22	34.29
3	27.42	23	32.09
4	24.12	24	24.89
5	41.44	25	25.67
6	34.94	26	33.78
7	25.32	27	38.61
8	41.14	28	37.23
9	37.36	29	31.31
10	31.64	30	26.39
11	41.42	31	24.39
12	37.53	32	42.99
13	23.34	33	32.69
14	36.43	34	38.16
15	31.81	35	36.49
16	33.65	36	42.87
17	33.88	37	41.54
18	38.19	38	28.61
19	24.79	39	37.37
20	24.81	40	30.22

You are required to summarise this data and calculate the following:

·       the mean strength

·       the median strength

·       the standard deviation for the results

·       the percentage of blocks which fall between +/- one standard deviation

·       estimate the probability that the strength of a given concrete cube will exceed 37 N/mm² 

·       apply binomial distribution methods to determine the probability of testing a cube which will exceed

37 N/mm² within the next 5 tests.

Answer 1

Mean: add values and divide by number of values in set

Median: middle value when in order from least to greatest.

For standard deviation:

Find mean,

for each number, subtract the mean and square the result,

the average of the squared differences is the SD

To find +/- 1 SD:

We can use the empirical rule to determine the answer. The rule states that about 68% of the area under a normal distribution falls inside one standard deviation away from the mean. Normal distribution / 2.

Or you can take the SD / mean * 100 =