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8.07 Further applications of the normal distribution

Interactive practice questions

The operating times of phone batteries are approximately normally distributed with mean $34$34 hours and a standard deviation of $4$4 hours. Answer the following questions using your calculator:

a

Approximately what percentage of batteries last between $33$33 and $38$38 hours?

Round your answer to the nearest percent.

b

Approximately what percentage of batteries last between $28$28 hours and $41$41 hours?

c

Any battery that lasts less than $23$23 hours is deemed faulty. If a company manufactured $51000$51000 batteries, approximately how many batteries would they be able to sell? Round your answer to the nearest integer.

Medium
1min

The height of sunflowers is approximately normally distributed, with a mean height of $1.6$1.6 m and a standard deviation of $8$8 cm.

Medium
1min

In the Maths Methods course at Winter Heights High, the mean mark for the year was $62%$62% and the standard deviation was $13%$13%.

Medium
3min

The length of the tail of a domestic cat is normally distributed with a mean of $25$25 cm and a standard deviation of $2.2$2.2 cm.

Use the capabilities of your CAS calculator to answer the following, rounding your answers to three decimal places:

Medium
9min
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Outcomes

ACMMM167

understand the effects of linear changes of scale and origin on the mean and the standard deviation

ACMMM169

recognise features of the graph of the probability density function of the normal distribution with mean μ and standard deviation σ and the use of the standard normal distribution

ACMMM170

calculate probabilities and quantiles associated with a given normal distribution using technology, and use these to solve practical problems

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