Question

assume that a randomly selected subject is given a bone density test. those test scores are normally distributed with a mean of 0 and a standard deviation of 1. draw a graph and find the probability of a bone density test score between - 1.98 and 1.98.
sketch the region. choose the correct graph below.
a.
b.
c.
d.
the probability is □.
(round to four decimal places as needed.)

Explanation:

Step1: Use the property of the standard normal distribution

For a standard normal distribution \(Z\sim N(0,1)\), the probability \(P(-1.98 < Z<1.98)\) can be calculated using the formula \(P(-a < Z < a)=2\Phi(a)-1\), where \(\Phi(z)\) is the cumulative - distribution function of the standard normal distribution.

Step2: Look up the value of \(\Phi(1.98)\)

From the standard - normal table, \(\Phi(1.98) = 0.9761\).

Step3: Calculate \(P(-1.98 < Z < 1.98)\)

Substitute \(\Phi(1.98)\) into the formula \(P(-1.98 < Z < 1.98)=2\times0.9761 - 1\).

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Answer:

\(0.9522\)