Question

For all problems drawing a normal curve is also needed, please!

6. The top 7% of applicants (as measured by SAT scores) will receive scholarships. Suppose GRE score is normally distributed with mean 500 and standard deviation 100. How high does your GRE score have to be to qualify for a scholarship?

7. Family income is normally distributed with mean $25000 and standard deviation $12000 If the poverty level is $10,000, what percentage of the population lives in poverty?

8. If a fair coin is tossed 70 times. Find the probability of getting more than 40 heads.

9. The engines made by Ford for speedboats had an average power of 220 horsepower (HP) and standard deviation of 15 HP. A potential buyer intends to take a sample of four engines and will not place an order if the sample mean is less than 215 HP. What is the probability that the buyer will not place an order?

Answer 1

6) P(X > x) = 0.07

or, P((X - )/ > (x - )/) = 0.07

or, P(Z > (x - 500)/100) = 0.07

or, P(Z < (x - 500)/100) = 0.93

or, (x - 500)/100 = 1.48

or, x = 1.48 * 100 + 500

or, x = 648

7) P(X < 10000)

= P((X - )/ < (10000 - )/)

= P(Z < (10000 - 25000)/12000)

= P(Z < -1.25)

= 0.1056

8) n = 70

   p = 0.5

= n * p = 70 * 0.5 = 35

= sqrt(np(1 - p)

     = sqrt(70 * 0.5 * 0.5) = 4.1833

P(X > 40)

= P(X > 40.5)

= P((X - )/> (40.5 - )/)

= P(Z > (40.5 - 35)/4.1833)

= P(Z > 1.31)

= 1 - P(Z < 1.31)

= 1 - 0.9049

= 0.0951

9) P( < 215)

= P(( - )/() < (215 - )/())

= P(Z < (215 - 220)/(15/))

= P(Z < -0.67)

= 0.2514