an employee is taxed 6.2 percent of their gross pay for Social Security, up to $127,200. After an employee has earned that much, Social Security payments are no longer deducted for the remainder of the year.

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The number of books borrowed from a library each week follows a normal distribution. When a sample is taken for several weeks, t

Marat540 [252]

$\mathbb P(X>250)=\mathbb P\left(\dfrac{X-190}{30}>\dfrac{250-190}{30}\right)=\mathbb P(Z>2)\approx0.0228$

Or, if you're familiar with the empirical rule and the basic properties of the normal distribution, you can use the fact that approximately $95/%$ of the distribution lies within two standard deviations of the mean, or

$\mathbb P(|Z|$

which means about $5\%$ of the distribution lies outside this interval, or

$\mathbb P((-22))\approx0.05$

Because the distribution is symmetric, you have

$\mathbb P(-22)$
$\implies \mathbb P((-22))=\mathbb P(-22)=2\mathbb P(Z>2)\approx0.05$
$\implies \mathbb P(Z>2)\approx 0.025$