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.

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

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.

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

4.2 Statistical distributions (A-level only)

Question 18

Markscheme

4.2 Statistical distributions (A-level only)

Question 18

Markscheme

4.2 Statistical distributions (A-level only)

Question 18

4.2 Statistical distributions (A-level only) Questions

4.2 Statistical distributions (A-level only)

Question 18

4.2 Statistical distributions (A-level only) Questions