Question

# 9. The time for a certain male student to commute to SCSU is Normally Distributed with...

9.

The time for a certain male student to commute to SCSU is Normally Distributed with mean 48.3 minutes and standard deviation of 7.1 minutes. A random sample of 25 commuting times is taken.

Find the 80th percentile of the sample mean of the commuting times.

10.

The time for a certain male student to commute to SCSU is Normally Distributed with mean 48.3 minutes and standard deviation of 7.1 minutes. A random sample of 25 commuting times is taken.

Find the value t such that 6% of the sample means of the commuting times is greater than t.

a)

X ~ N ( µ = 48.3 , σ = 7.1 )
80th percentile = P ( < x ) = 80% = 0.8
To find the value of x
Looking for the probability 0.8 in standard normal table to calculate Z score = 0.8416
Z = ( X - µ ) / ( σ / √(n) )
0.8416 = ( X - 48.3 ) / ( 7.1/√(25) )
X = 49.4951

b)

P( > t) = 0.06

X ~ N ( µ = 48.3 , σ = 7.1 )
P ( X > t ) = 1 - P ( X < t ) = 1 - 0.06 = 0.94
To find the value of t
Looking for the probability 0.94 in standard normal table to calculate Z score = 1.5548
Z = (t - µ ) / ( σ / √(n) )
1.5548 = ( X - 48.3 ) / (7.1/√(25))
t = 50.5078