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In: Statistics and Probability

Q3.(15) The SAT scores for US high school students are normally distributed with a mean of...

Q3.(15) The SAT scores for US high school students are normally distributed with a mean of 1500 and a standard deviation of 100.

1.(5) Calculate the probability that a randomly selected student has a SAT score greater than 1650.

2.(5) Calculate the probability that a randomly selected student has a SAT score between 1400 and 1650, inclusive.

3.(5) If we have random sample of 100 students, find the probability that the mean scores between 1485 and 1510, inclusive.

Solutions

Expert Solution

Solution :

1.

P(x > 1650) = 1 - P(x < 1650)

= 1 - P[(x - ) / < (1650 - 1500) / 100)

= 1 - P(z < 1.5)

= 1 - 0.9332

= 0.0668

Probability = 0.0668

2.

P(1400 < x < 1650) = P[(1400 - 1500)/ 100) < (x - ) /  < (1650 - 1500) / 100) ]

= P(-1 < z < 1.5)

= P(z < 1.5) - P(z < -1)

= 0.9332 - 0.1587

= 0.7745

Probability = 0.7745

3.

= / n = 100 / 100 = 10

= P[(1485 - 1500) / 10 < ( - ) / < (1510 - 1500) / 10)]

= P(-1.5 < Z < 1)

= P(Z < 1) - P(Z < -1.5)

= 0.8413 - 0.0668

= 0.7745

Probability = 0.7745

orchestra answered 1 year ago
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