Question

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.

Answer #1

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**

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