The 1300 train from Jahor to Keman runs every day. The probability that the train arrives late in Keman is $$$0.35$$$. A random sample of 142 days is taken. Use an approximation to find the probability that the train arrives late on more than 40 days. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w20_qp_53 Year：2020 Question No：4(b)

Answer:

Mean $=142 \times 0.35=49.7$
Variance $=142 \times 0.35 \times 0.65=32.305$
$\mathrm{P}(X>40)=\mathrm{P}\left(z>\frac{40.5-49.7}{\sqrt{32.305}}\right)$
$\mathrm{P}(z>-1.619)$
$0.947$

Knowledge points:

5.5.3 recall conditions under which the normal distribution can be used as an approximation to the binomial distribution, and use this approximation, with a continuity correction, in solving problems. (n sufficiently large to ensure that both np > 5 and nq > 5.)

Answer:

Knowledge points:

Solution:

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