The probability that a single randomly selected value is between 184 and 205.1 is,

\(\displaystyle{P}{\left({184}{<}{X}{<}{205.1}\right)}={P}{\left({\frac{{{184}-{198.8}}}{{{69.2}}}}{<}{\frac{{{X}-\mu}}{{\sigma}}}{<}{\frac{{{205.1}-{198.8}}}{{{69.2}}}}\right)}\)</span>

\(\displaystyle={P}{\left(-{0.214}{<}{z}{<}{0.091}\right)}\)</span>

\(\displaystyle={P}{\left({z}{<}{0.091}\right)}-{P}{\left({z}{<}-{0.214}\right)}\)</span>

The probability of z less than 0.091 can be obtained using the excel formula “=NORM.S.DIST(0.091,TRUE)”. The probability value is 0.5363.

The probability of z less than –0.214 can be obtained using the excel formula “=NORM.S.DIST(–0.214,TRUE)”. The probability value is 0.4153.

The required probability value is,

\(\displaystyle{P}{\left({184}{<}{X}{<}{205.1}\right)}={P}{\left({z}{<}{0.091}\right)}-{P}{\left({z}{<}-{0.214}\right)}\)</span>

\(\displaystyle={0.5363}−{0.4153}={0.1210}\)

Thus, the probability that a single randomly selected value is between 184 and 205.1 is 0.1210.