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[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

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[ACTION NAME]

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# Your action step 2

# Your action step 3

...

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The height of a public bus door is designed to ensure that the probability of a man hitting his head is no higher than 0.0228. Assuming the height of men, $X$, follows a normal distribution $N(170, 49)$ (measured in cm, where 170 is the mean and 49 is the variance), and referring to the following probabilities: 
$P(\mu - \sigma < X \leq \mu + \sigma) = 0.6826$, 
$P(\mu - 2\sigma < X \leq \mu + 2\sigma) = 0.9544$, 
$P(\mu - 3\sigma < X \leq \mu + 3\sigma) = 0.9974$,
determine the minimum height at which the bus door should be designed (measured in cm).

Present the answer in LaTex format: \boxed{Your answer}
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