Singapore aims to be one of the world’s most livable countries. In our urban living, noise pollution from transportation imposes a challenge to this goal. Sound is measured in frequency by Hertz (Hz) and loudness by Decibel (dB).

A person with perfect hearing can sense low-frequency sound at 20 Hz from a rumbling drum, to high frequency at 20 kHz sharper than mosquito buzzing. Sound loudness levels can be soft like leaves rustling at 20 dB, or loud like rock concert at 120dB.

Our abilities to hear high frequency and detect sound volume will deteriorate as we age. Furthermore, constant exposure to noise beyond 90 dB will cause gradual damage to our hearing organ. Noise pollution not only affect our hearing, but will also affect our emotions.

Assuming Efficient Bus Service (EBS) was contracted by Land Transport Authority (LTA) since eight years ago to operate bus services in the country. As a good corporate citizen, EBS’s senior management feels it has the responsibility to reduce noise caused by its vehicles.

(a) A person with a hearing loss of 40 dB is considered to have moderate hearing impairment. Statistics shows that the age a person starts to have moderate hearing impairment follows a Normal Distribution with a mean of 61.5 years old with a standard deviation of 4.8 years.

Note: You shall use relevant Statistics formula and Standard Normal Distribution table to work on Q1(a). (i) Find the age (to 2 decimal places) that 10% of the people have not suffered from moderate hearing impairment yet.