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Standard level

8.03 Further applications of 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

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

The weights of babies born in a hospital in Sydney are considered normally distributed with a mean of $3.3$3.3 kg and a standard deviation of $0.50$0.50 kg.

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

Medium
6min
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