Question

In: Statistics and Probability

If μ = 100, σ = 12, and n = 16, then use the t distribution...

If μ = 100, σ = 12, and n = 16, then use the t distribution to evaluate the probability ?̅ exceeds 103? Express your answer as a percentage with 3 decimals.

Solutions

Expert Solution

Solution :

mean = = 100

standard deviation = = 12

n = 16

=   = 100

= / n = 12 / 16 = 3

P( > 103) = 1 - P( < 103)

= 1 - P[( - ) / < (103 - 100) / 3]

= 1 - P(z < 1)

Using z table,    

= 1 - 0.8413

= 0.1587

The percentage is 15.87%


Related Solutions

If u = 100, sigma = 12, and n = 16, then use the t distribution...
If u = 100, sigma = 12, and n = 16, then use the t distribution to evaluate the probability ? exceeds 103? Express your answer as a percentage with 3 decimals
Suppose x has a distribution with μ = 16 and σ = 10. (a) If a...
Suppose x has a distribution with μ = 16 and σ = 10. (a) If a random sample of size n = 45 is drawn, find μx, σ x and P(16 ≤ x ≤ 18). (Round σx to two decimal places and the probability to four decimal places.) μx = σ x = P(16 ≤ x ≤ 18) = (b) If a random sample of size n = 72 is drawn, find μx, σ x and P(16 ≤ x ≤...
Suppose x has a distribution with μ = 12 and σ = 8. (a) If a...
Suppose x has a distribution with μ = 12 and σ = 8. (a) If a random sample of size n = 33 is drawn, find μx, σx and P(12 ≤ x ≤ 14). (Round σx to two decimal places and the probability to four decimal places.) μx = σx = P(12 ≤ x ≤ 14) = (b) If a random sample of size n = 61 is drawn, find μx, σx and P(12 ≤ x ≤ 14). (Round σx...
Suppose x has a distribution with μ = 12 and σ = 9. A.) If a...
Suppose x has a distribution with μ = 12 and σ = 9. A.) If a random sample of size n = 35 is drawn, find μx, σx and P(12 ≤ x ≤ 14). (Round σx to two decimal places and the probability to three decimal places.) P(12 ≤ x ≤ 14)= B.) If a random sample of size n = 62 is drawn, find μx, σx and P(12 ≤ x ≤ 14). (Round σx to two decimal places and...
Suppose x has a distribution with μ = 12 and σ = 7. (a) If a...
Suppose x has a distribution with μ = 12 and σ = 7. (a) If a random sample of size n = 31 is drawn, find μx, σx and P(12 ≤ x ≤ 14). (Round σx to two decimal places and the probability to four decimal places.) μx = σx = P(12 ≤ x ≤ 14) = (b) If a random sample of size n = 75 is drawn, find μx, σx and P(12 ≤ x ≤ 14). (Round σx...
Suppose x has a distribution with μ = 17 and σ = 12. (a) If a...
Suppose x has a distribution with μ = 17 and σ = 12. (a) If a random sample of size n = 33 is drawn, find μx, σx and P(17 ≤ x ≤ 19). (Round σx to two decimal places and the probability to four decimal places.) P(17 ≤ x ≤ 19) = (b) If a random sample of size n = 71 is drawn, find μx, σx and P(17 ≤ x ≤ 19). (Round σx to two decimal places...
Suppose x has a distribution with μ = 12 and σ = 5. (a) If a...
Suppose x has a distribution with μ = 12 and σ = 5. (a) If a random sample of size n = 31 is drawn, find μx, σx and P(12 ≤ x ≤ 14). (Round σx to two decimal places and the probability to four decimal places.) μx = σx = P(12 ≤ x ≤ 14) = (b) If a random sample of size n = 67 is drawn, find μx, σx and P(12 ≤ x ≤ 14). (Round σx...
1. Given a normal distribution with μ=102 and σ=25, if you select a sample of n=12,...
1. Given a normal distribution with μ=102 and σ=25, if you select a sample of n=12, what is the probability that ?̅ is a. less than 90 ? b. between 90 and 92.5 ? c. above 103.6 ? 2. Given a normal distribution with μ=101 and σ=15, if you select a sample of n=9, what is the probability that ?̅ is a. less than 95 ? b. between 90 and 92.5 ? c. above 101.8 ?
(5) Suppose x has a distribution with μ = 20 and σ = 16. (a) If...
(5) Suppose x has a distribution with μ = 20 and σ = 16. (a) If a random sample of size n = 47 is drawn, find μx, σx and P(20 ≤ x ≤ 22). (Round σx to two decimal places and the probability to four decimal places.) μx = σ x = P(20 ≤ x ≤ 22)= (b) If a random sample of size n = 61 is drawn, find μx, σx and P(20 ≤ x ≤ 22). (Round...
A normal distribution has a mean of μ = 80 with σ = 12. Find the...
A normal distribution has a mean of μ = 80 with σ = 12. Find the following probabilities. (a) p(X > 83) (b) p(X < 74) (c) p(X < 92) (d) p(71 < X < 89)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT