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2.4.2 The Normal distribution (A-level only)

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Question 22

A viticulturist is investigating the survival of a new hybrid vine graft. The probability that a graft is successful is denoted by $p$ . A sample of 100 grafts is taken, and the random variable $S\,$ represents the number of successful grafts, where $\sim \text{B}(100, p)$ .

Using a normal approximation, the probability that $S\,$ is at least 53 is 0.0054 to 4 decimal places.

Show that $p\,$ satisfies $426.01p^2 - 446.01p + 110.25 = 0$ when normal probability tables are used.

[6]

ii.

Hence find the value of $p$ , justifying your answer.

[2]

Markscheme

2.4.2 The Normal distribution (A-level only) Questions

A Level
Maths
2.4.2 The Normal distribution (A-level only)

351 exam-style questions on AQA A Level Maths 2.4.2 The Normal distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

2.4.2 The Normal distribution (A-level only)

Question bank

2.4.2 The Normal distribution (A-level only)

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Question 22

Using a normal approximation, the probability that $S\,$ is at least 53 is 0.0054 to 4 decimal places.

Show that $p\,$ satisfies $426.01p^2 - 446.01p + 110.25 = 0$ when normal probability tables are used.

[6]

ii.

Hence find the value of $p$ , justifying your answer.

[2]

Markscheme

2.4.2 The Normal distribution (A-level only) Questions

A Level
Maths
2.4.2 The Normal distribution (A-level only)

351 exam-style questions on AQA A Level Maths 2.4.2 The Normal distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.