A company sells seeds and claims that 55% of its pea seeds germinate - Edexcel - A-Level Maths Statistics - Question 5 - 2017 - Paper 2

Let S = number of seeds out of 24 that germinate, S ~ B(24, 0.55).

T = number of trays with at least 15 germinating, T ~ B(10, p).

To find this probability:

1. Calculate the probability for a single tray, P(S ≥ 15).

2. Use the cumulative distribution function to compute P(T ≥ 5):

   $P(T ext{ ≥ } 5) = 1 - P(T < 5)$

   With appropriate computations, we get approximately 0.149.

1. The sample size n is large.
2. The probability p is close to 0.5.

Let X ~ N(μ, σ²) where μ = np = 240 × 0.55 = 132 and σ² = np(1-p) = 240 × 0.55 × 0.45 = 59.4.

To find P(X ≥ 150), apply continuity correction:

$P(X > 149.5) = P\left(Z > \frac{149.5 - 132}{\sqrt{59.4}}\right)$

This calculation results in ≈ 0.01158, which approximates to 0.0116.

Since the calculated probability is very small, there is evidence to suggest that the company's claim is incorrect.