Scores on the SAT form a normal distribution with a mean of µ = 500 with σ = 100. If the state college only accepts students who score in the top 60% on the SAT, what is the minimum score needed to be accepted?

1 answer

Question:

Scores on the SAT form a normal distribution with a mean of µ = 500 with σ = 100. If the state college only accepts students who score in the top 60% on the SAT, what is the minimum score needed to be accepted?

Answer:The minimum score needed to be accepted is 525.3.Step-by-step explanation:Problems of normally distributed samples are solved using the z-score formula.In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:[tex]Z = \frac{X - \mu}{\sigma}[/tex]The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.In this problem, we have that:[tex]\mu = 500, \sigma = 100[/tex]If the state college only accepts students who score in the top 60% on the SAT, what is the minimum score needed to be accepted?The 60th percentile, which is the value of X when Z has a pvalue of 0.6. So it is X when Z = 0.253. So[tex]Z = \frac{X - \mu}{\sigma}[/tex][tex]0.253 = \frac{X - 500}{100}[/tex][tex]X - 500 = 0.253*100[/tex][tex]X = 525.3[/tex]The minimum score needed to be accepted is 525.3.

Calculate the change in enthalpy (LaTeX: \DeltaΔH) of a reaction with the following information:
Energy of Reactants = 129 kJ
Energy of the Products = 110 kJ
Energy of the Transition State = 198 kJ...

An 11-inch candle and a 15-inch candle are lit. The 11-inch candle burns 0.5
inches every hour. The 15-inch candle burns 2 inches every hour. Write an
equation that can be used to find h, the number of hours it will take until the
candles are the same height?
Enter your answer in the space provided....