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4.5.1 Statistical distributions (A-level only)

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Question 6

The random variable XXX has a normal distribution with mean 12 and standard deviation 4.

a.

Find P(X<14)P(X < 14)P(X<14).

[2]
b.

Find the value of kkk such that

P(12−k<X<12+k)=0.80 P(12 - k < X < 12 + k) = 0.80 P(12−k<X<12+k)=0.80
[4]
c.

A single observation xxx, of XXX, is to be taken. A rectangle is drawn on a centimetre grid with vertices having coordinates (0,0)(0, 0)(0,0), (x,0)(x, 0)(x,0), (x,x−4)(x, x-4)(x,x−4) and (0,x−4)(0, x-4)(0,x−4).

Find the probability that the area of this rectangle is more than 45 cm245\text{ cm}^245 cm2.

[4]

4.5.1 Statistical distributions (A-level only) Questions

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