← Back to Chapter
Subchapter overview
Browsing as Guest. Answer checking, progress and bookmarks are disabled. Log in to track your work.

Practice — Statistics bridge for Further Mathematics • 0.7 Normal distribution

All 10 Unsolved 10 Solved 0 Attempted 0
01 02 03 04 05 06 07 08 09 10
1. Reading the variance parameter
Difficulty: ★☆☆
2154

\(X\sim\mathrm{N}(32,49)\), where the second parameter is the variance. What is the standard deviation of \(X\)?

Hint
Variance is the square of standard deviation.
Log in to check answers and record progress. You can still view solutions.
2. Symmetry at the mean
Difficulty: ★☆☆
2155

\(X\sim\mathrm{N}(72,25)\). Find \(P(X<72)\).

Hint
Locate 72 relative to the centre of the normal curve.
Log in to check answers and record progress. You can still view solutions.
3. Standardising a value
Difficulty: ★☆☆
2156

\(X\sim\mathrm{N}(100,225)\). Which standard normal value corresponds to \(X=130\)?

Hint
Subtract the mean and divide by the square root of the second parameter.
Log in to check answers and record progress. You can still view solutions.
4. A normal upper tail
Difficulty: ★★☆
2157

The mass \(M\) of a packet has model \(\mathrm{N}(48,36)\), in grams. Find \(P(M>57)\), to 4 d.p.

Hint
The packet standard deviation is 6 g; shade the area to the right of 57 g.
Log in to check answers and record progress. You can still view solutions.
5. An interval crossing the mean
Difficulty: ★★☆
2158

\(X\sim\mathrm{N}(20,16)\). Find \(P(14<X<22)\), to 4 d.p.

Hint
Convert both endpoints to standard normal values, then subtract cumulative areas.
Log in to check answers and record progress. You can still view solutions.
6. An inverse upper-tail cutoff
Difficulty: ★★☆
2159

The fill volume \(V\) of a bottle has model \(\mathrm{N}(250,16)\), in millilitres. Find the cutoff \(c\) such that \(P(V>c)=0.025\). Give \(c\) to 1 d.p.

Hint
An upper 2.5% tail leaves 97.5% of the area to the left.
Log in to check answers and record progress. You can still view solutions.
7. Recovering a standard deviation
Difficulty: ★★☆
2160

A normal variable has mean 40 and its 97.5th percentile is 49.8. Find its standard deviation, to 3 s.f.

Hint
Write the 97.5th percentile as the mean plus a standard normal percentile times the standard deviation.
Log in to check answers and record progress. You can still view solutions.
8. A strict inequality and continuity correction
Difficulty: ★★☆
2161

\(X\sim\mathrm{B}(120,0.25)\). Use \(Y\sim\mathrm{N}(30,22.5)\) as a normal approximation. Which region should be used to estimate \(P(X>35)\)?

Hint
First identify the smallest integer allowed by \(X>35\).
Log in to check answers and record progress. You can still view solutions.
9. Two symmetric percentiles
Difficulty: ★★★
2162

A normal variable has 20th percentile 12 and 80th percentile 30. Which pair gives its mean and standard deviation, each to 3 s.f.?

Hint
The 20th and 80th percentiles are symmetric about the mean; add and subtract their equations.
Log in to check answers and record progress. You can still view solutions.
10. A corrected two-sided binomial interval
Difficulty: ★★★
2163

\(X\sim\mathrm{B}(160,0.4)\). Use a normal approximation with continuity correction to estimate \(P(58\le X\le70)\), to 4 d.p.

Hint
Match the binomial mean and variance, then move both inclusive endpoints outward by half a unit.
Log in to check answers and record progress. You can still view solutions.
No questions left in this filter.