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**Hint:**Whenever in any situation, condition or terms are given and distribution is provided and it follows normal distribution then mean is represented as mu (ยต) and standard deviation, sigma (๐). The graph so obtained is symmetrical.

**Complete step-by-step answer:**Given

Scores on test are normally distributed

Mean (ยต) = 500

Standard deviation (๐) = 100

For getting admission he should score better than at least 70 % of students

So he should be in the remaining 30 % of students who have scored good marks.

We will find who have scored below the marks scored by tom

We will find probability of students who scored Marks below 585 marks

x < 585

we have to find the Z REGION

$\Rightarrow Z\, = \dfrac{{x - \mu }}{\sigma }$

For x = 585

$

\Rightarrow Z\, = \,\dfrac{{585\, - \,500}}{{100}} \\

\Rightarrow Z = \,\dfrac{{85}}{{100}} \\

\Rightarrow Z\, = \,0.85 \\

$ 0.85

Applying probability

P(Z < 0.85) = P(Z < 0) + P(0< Z <0.85)

p(Z<0) = 0.5

P(0< Z <0.85) = 0.3023 { from Z table at Z values normal distribution}

P(Z < 0.85) = 0.5 + 0.3023 = 0.8023

Changing this probability into percentage = $\dfrac{{0.8023}}{{100}}\, = \,80.23\,\% $

Therefore tom has to score more than 80.23%

**Option (D) is correct.**

**Note:**As it was mentioned, normal distribution so we will calculate z and probability as per condition. While calculating z values from the z table. Be extra attentive, change in a decimal value at any place can change your whole observation.

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