Question

In: Statistics and Probability

Use the normal distribution of SAT critical reading scores for which the mean is 509 and...

Use the normal distribution of SAT critical reading scores for which the mean is 509 and the standard deviation is 121. Assume the variable x is normally distributed. left parenthesis a right parenthesis What percent of the SAT verbal scores are less than 650? left parenthesis b right parenthesis If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 550?

Expert Solution

X ~ Normal(509,121²)

(a)

The following information has been provided:

μ=509, σ=121

We need to compute Pr(X≤650). The corresponding z-value needed to be computed:

Therefore,

The following is obtained graphically:

(b)

The following information has been provided:

μ=509, σ=121

We need to compute Pr(X≥550). The corresponding z-value needed to be computed is:

Therefore, we get that

The following is obtained graphically:

Out of 1000, we would expect 1000*0.3674 = 367 to have scores greater than 550.

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orchestra answered 2 years ago

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