Question

The scores of the students on a standardized test are normally distributed, with a mean of 500 and a standard deviation of 110. What is the probability that a randomly selected student has a score between 350 and 550? Use the portion of the standard normal table below to help answer the question.

Answer 1

...it's 59%

Explanation:

Just convert the decimal into a percent..round up.

Answer 2

The probability that a randomly selected student has a score between 350 and 550 is 0.5867

Explanation:

We know that,

`Z=(X-\mu)/(\sigma)`

where,

Z = Z score,

X = raw score,

μ = mean,

σ = standard deviation,

The probability that a randomly selected student has a score between 350 and 550 is,

`P(350<X<550)\\\\=P(350-500<X-500<550-500)`

`=P\left((350-500)/(110)<(X-500)/(110)<(550-500)/(110)\right)`

`=P\left(-1.36<Z<0.45\right)`

`=P(Z<0.45)-P(Z<-1.36)`

`=0.6736-0.0869`

`=0.5867`