Practice section 2 of 7

The marks of a large number of examination candidates are normally distributed with mean 45 and standard deviation 10. A candidate obtains a distinction by scoring x marks or more. If less than 5% obtain a distinction, find the range of x, correct to 1 decimal place.

The source labels this again as Example 4 (Self-directed Learning). For $Z\sim N(0,1)$, find (i) $P(0.32<Z\le 1.3)$ and (ii) a such that $P(Z<a)=0.156$.

For $Z\sim N(0,1)$, find (i) $P(-2.56<Z\le 0.134)$, (ii) $P(Z>1.863)$ and (iii) $P(|Z|>0.754)$.

If $X\sim N(\mu,6^2)$ and $P(X>82)=0.0478$, find μ.

Blue Neon Guppy masses at Green Park Tropical Fish Farm are normal with mean μ g and standard deviation σ g.5% exceed 85 g and 10% are below 25 g. Find μ and σ, then find the range symmetric about the mean containing 75% of the masses.

A student scored 60% in test 1 and 65% in test 2. The source models the respective scores as $X\sim N(55,15)$ and $Y\sim N(63,12)$. Did the student perform better relative to peers in the second test?