Question

The time, T minutes, taken to complete a jigsaw puzzle can be modelled by a normal distribution with mean μ and standard deviation 8.6.

It is found that 30% of times taken to complete the jigsaw puzzle are longer than 36.8 minutes.
By stating and solving an appropriate equation, show, correct to two decimal places, that mu =32.29.

Answer 1

To find the mean, we can use the z-score formula. The z-score formula is given by z = (x - mu) / sigma, where x is the observed value, mu is the mean, and sigma is the standard deviation. In this case, we are given that 30% of times taken to complete the jigsaw puzzle are longer than 36.8 minutes. We can use the z-score formula to find the z-score corresponding to the 30th percentile. We then use the z-score to find the corresponding value of x and solve for mu.

Step-by-step explanation:

To find the mean, μ, we can use the z-score formula. The z-score formula is given by z = (x - μ) / σ, where x is the observed value, μ is the mean, and σ is the standard deviation. In this case, we are given that 30% of times taken to complete the jigsaw puzzle are longer than 36.8 minutes. We can use the z-score formula to find the z-score corresponding to the 30th percentile. We then use the z-score to find the corresponding value of x and solve for μ.

Let's do the calculations:

First, we find the z-score corresponding to the 30th percentile, which is -0.5244 (rounded to 4 decimal places).

Next, we use the z-score formula to find the corresponding value of x:

-0.5244 = (36.8 - μ) / 8.6

Solving for μ, we get μ = 32.29 (rounded to 2 decimal places).