2.4.12 Calculate probabilities from a Normal distribution (A-level only)

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Question 88

A tech logistics company monitors the flight duration of its delivery drones. The flight duration during the summer, $S\,$ minutes, is modelled by a normal distribution $\sim \text{N}(320, 24^2)$ .

Using standardisation and showing your working, determine the probability that, for a drone flight selected at random in the summer,

(i) the duration exceeds 284 minutes,

(ii) the duration is 320 minutes, correct to the nearest 16 minutes.

[5]

The flight duration during the winter, $W\,$ minutes, is modelled by $\sim \text{N}(\mu, \sigma^2)$ .

Given that $P(W>280)=0.0901\text{P}(W > 280) = 0.0901$ and $P(W<220)=0.2810\text{P}(W < 220) = 0.2810$ ,

(i) find two linear equations in terms of $\mu\,$ and $σ\sigma$ ,

(ii) hence, showing your working, calculate the value of $\mu\,$ and the value of $σ\sigma$ .

[5]

A tech logistics company monitors the flight duration of its delivery drones. The flight duration during the summer, $S\,$ minutes, is modelled by a normal distribution $\sim \text{N}(320, 24^2)$ .

Using standardisation and showing your working, determine the probability that, for a drone flight selected at random in the summer,

(i) the duration exceeds 284 minutes,

(ii) the duration is 320 minutes, correct to the nearest 16 minutes.

[5]

The flight duration during the winter, $W\,$ minutes, is modelled by $\sim \text{N}(\mu, \sigma^2)$ .

Given that $P(W>280)=0.0901\text{P}(W > 280) = 0.0901$ and $P(W<220)=0.2810\text{P}(W < 220) = 0.2810$ ,

(i) find two linear equations in terms of $\mu\,$ and $σ\sigma$ ,

(ii) hence, showing your working, calculate the value of $\mu\,$ and the value of $σ\sigma$ .

2.4.12 Calculate probabilities from a Normal distribution (A-level only)

Question 88

Markscheme

2.4.12 Calculate probabilities from a Normal distribution (A-level only)

Question 88

Markscheme

2.4.12 Calculate probabilities from a Normal distribution (A-level only)

Question 88

2.4.12 Calculate probabilities from a Normal distribution (A-level only) Questions

2.4.12 Calculate probabilities from a Normal distribution (A-level only)

Question 88

2.4.12 Calculate probabilities from a Normal distribution (A-level only) Questions