# Determining minimum probability for a standardised variable using the Chebyshev inequality [duplicate]

A report on rural water resources states that the nitrate level of wells in a certain groundwater system has a probability distribution whose mean and standard deviation are 5.2, 2.1 ppm, respectively. From the Chebyshev inequality, determine the minimum probability that a well in this system will have a nitrate level between 0.4 and 10.0 ppm.

For a standardised random variable Y corresponding to a random variable X:

$Y = \frac{X - E\left \{ X \right \}}{\sigma\left \{ X \right \}}$

Any hints to further my attempt is much appreciated.

## marked as duplicate by whuber♦ distributions StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Aug 26 '18 at 15:21
• This seems to be two different questions. Are you asking about the question you have quoted or are you trying to ask something about your data Y? If it's the latter, what are you asking? – whuber Aug 25 '18 at 13:31