SOLUTION: The scores on a college entrance examination are normally distributed with a mean of 550 and standard deviation of 100. For a sample of 30 students, what is the probability tha

Algebra ->  Probability-and-statistics -> SOLUTION: The scores on a college entrance examination are normally distributed with a mean of 550 and standard deviation of 100. For a sample of 30 students, what is the probability tha      Log On


   

Question 1152775: The scores on a college entrance examination are normally distributed with a mean of 550 and standard deviation of 100.
For a sample of 30 students, what is the probability that the sample has a mean between 500-575?
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
z1 = %28575+-+550%29%2F%28100%2Fsqrt%2830%29%29 = 1.37

z2 = %28500+-+550%29%2F%28100%2Fsqrt%2830%29%29 = -2.74

Look up 1.37 on a z-table. You get 0.9137. This is the probability the mean score is less than 575.

Look up -2.74 on a z-table. You get 0.0031. This is the probability the mean score is less than 500.

To find the probability that the mean score is between 500 and 575, simply subtract 0.0031 from 0.9137. You get an answer of 0.9106.

This means there is a 0.9106 probability that the mean score is between 500 and 575.