2.4.2 The Normal distribution (A-level only)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64

Question 35

A geomechanical boring tool is used to create pilot holes for foundation piles. The depth, $D$ millimetres, achieved in a single standard operation of the tool is normally distributed with mean $500$ and standard deviation $20$ .

Using standardisation, show that the probability that an operation results in a depth of less than $\text{ mm}$ is $0.3446$ .

[3]

A specific site requirement necessitates a hole depth of at least $\text{ mm}$ . A technician is permitted up to 3 independent attempts at a single location to meet this requirement. If an attempt meets or exceeds the requirement, no further attempts are made at that location.

Given that the technician eventually successfully met the requirement at a location, determine the probability that success was achieved on the second attempt with a hole deeper than $\text{ mm}$ .

[4]

Using standardisation, show that the probability that an operation results in a depth of less than $\text{ mm}$ is $0.3446$ .

[3]

Given that the technician eventually successfully met the requirement at a location, determine the probability that success was achieved on the second attempt with a hole deeper than $\text{ mm}$ .

2.4.2 The Normal distribution (A-level only)

Question 35

Markscheme

2.4.2 The Normal distribution (A-level only)

Question 35

Markscheme

2.4.2 The Normal distribution (A-level only)

Question 35

2.4.2 The Normal distribution (A-level only) Questions

2.4.2 The Normal distribution (A-level only)

Question 35

2.4.2 The Normal distribution (A-level only) Questions