1 of 8 0-day streak

Mixed probability applications with the normal distribution

Question 1 of 8

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Use the following normal model for each trial

Let X be the length, in millimetres, of one manufactured component

The distribution is \(X\sim N\left(53,25\right)\)

The success event for one trial is the inequality shown here

A success is recorded when \(X>48\)

The process is repeated for \(7\) independent trials, with the same normal model used for each trial

Let \(Y\) be the number of successes in the \(7\) trials. The required event is \(Y=4\)

Use the one-trial success probability from the normal model as the probability for the second model

(a)1 mark

Which probability model should be used for the number of successes?

The count of successes should be modelled by a binomial distribution after the normal step

Use the boundary's standard score, rather than the normal area, as the binomial success probability

(b)1 mark

Find the probability that one trial is a success. Give the answer to 2 decimal places

Probability for one success Format: 2 d.p.

Let \(Y\) be the number of successes in the \(7\) trials. The required event is \(Y=4\)

Choose the calculation that matches the requested binomial quantity

Add terms for several success counts

Use the one binomial term for exactly 4 successes

(d)1 mark

Let \(Y\) be the number of successes in the \(7\) trials. The required event is \(Y=4\)

Calculate the probability that exactly the stated number of trials are successful. Give the answer to 4 decimal places

Binomial probability Format: 4 d.p.