According to the College Board, SAT mathematics scores from the 2014 school year for high school students in the United States were normally distributed with a mean of 513 and a standard deviation of 120. Use a standard normal table such as this one to determine the probability that a randomly chosen high school student who took the SAT in 2014 will have a mathematics SAT score between 400 and 750 points.

Answer:

80.25%

Explanation:

Data provided in the question

[tex]X \sim N (513,120)[/tex]

Mean = 513

Standard deviation = 120

Now

[tex]P(400 < x < 750) = P (\frac{400 - 513}{120} <z < \frac{750 - 513}{120})[/tex]

After solving this

= P (-0.9417 < Z < 1.975)

= P (-0.9417 < Z < 0) + P (0 < Z < 1.975)

= 0.3264 + 0.4761

or by apply the Z table or excel command

Like this

NORMSDIST(1.98) - NORMSDIST(-0.94)

= 0.9761 - 0.1736

= 80.25%

Hence the probability is 80.25%

C=59(F−32) The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true? A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 59 degree Celsius. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit. A temperature increase of 59 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius. A) I only B) II only C) III only D) I and II only