A quality control technician monitors the viscosity, $v$ centipoise (cP), of a batch of synthetic lubricant. The measured viscosity, $V$ cP, follows a normal distribution with mean $μ\mu$ cP and standard deviation $3.2$ cP.

Find the probability that a single measurement of the viscosity is within $2.4$ cP of the mean $μ\mu$ .

The technician takes a random sample of 64 independent measurements.

Determine the probability that the sample mean of these 64 results, $Vˉ\bar{V}$ , is within $0.6$ cP of $μ\mu$ .

Given that the mean of these 64 measurements is $412.5$ cP, calculate a $95%95\%$ confidence interval for $μ\mu$ , giving your limits to three decimal places.

Find the probability that a single measurement of the viscosity is within $2.4$ cP of the mean $μ\mu$ .

The technician takes a random sample of 64 independent measurements.

Determine the probability that the sample mean of these 64 results, $Vˉ\bar{V}$ , is within $0.6$ cP of $μ\mu$ .

Given that the mean of these 64 measurements is $412.5$ cP, calculate a $95%95\%$ confidence interval for $μ\mu$ , giving your limits to three decimal places.

2.4.6 Probabilities using the normal distribution (A-level only)

Question 51

Markscheme

2.4.6 Probabilities using the normal distribution (A-level only)

Question 51

Markscheme

2.4.6 Probabilities using the normal distribution (A-level only)

Question 51

2.4.6 Probabilities using the normal distribution (A-level only) Questions

2.4.6 Probabilities using the normal distribution (A-level only)

Question 51

2.4.6 Probabilities using the normal distribution (A-level only) Questions