To obtain information on the volume of freight shipped by tr

To obtain information on the volume of freight shipped by truck over a particular interstate highway, a state highway department monitored the highway for one hour periods randomly selected throughout a one-month period. The number of heavy-duty trailers per hour is approximately normally distributed with µ=50 and sd=7. Answer questions using this information.

1.What is the probability that the number of trucks for one-hour period would exceed 60?

(a)0.0021

(b)0.0764

(c)0.5000

(d)0.9236

(e)0.9979

2.What is the probability that average number of trailers for a four-hour period will be larger than 60?

(a)0.0021

(b)0.0764

(c)0.5000

(d)0.9236

(e)0.9979

3.What is the probability that the total number of trucks for a four-hour period would exceed 180?

(a)0.0021

(b)0.0764

(c)0.5000

(d)0.9236

(e)0.9979

4.We computed the probability of the test statistics fall in the rejection region when the false null hypothesis is tested. Which of the following we computed?

(a)beta=P(reject H₀ when H₀ is true)

(b)alpha= P(fail to reject H₀ when H₀ is false)

(c)Power=1-beta

(d)1-alpha

(e)all of the above

Solution

To obtain information on the volume of freight shipped by truck over a particular interstate highway, a state highway department monitored the highway for one hour periods randomly selected throughout a one-month period. The number of heavy-duty trailers per hour is approximately normally distributed with µ=50 and sd=7. Answer questions using this information.

1.What is the probability that the number of trucks for one-hour period would exceed 60?

(a)0.0021

(b)0.0764

(c)0.5000

(d)0.9236

(e)0.9979

z=(60-50)/7=1.43

P( x>60) = p( z >1.43)=0.0764

2.What is the probability that average number of trailers for a four-hour period will be larger than 60?

(a)0.0021

(b)0.0764

(c)0.5000

(d)0.9236

(e)0.9979

Se=7/sqrt(4)=3.5,    z=(60-50)/3.5=2.86

P( x >60) = p( z >2.86)=0.0021

3.What is the probability that the total number of trucks for a four-hour period would exceed 180?

(a)0.0021

(b)0.0764

(c)0.5000

(d)0.9236

(e)0.9979

Sum follows normal with 200 and sd =14

Z=(180-200)/14=-1.43

P( x >180)= P( z > -1.43) = 0.9236

4.We computed the probability of the test statistics fall in the rejection region when the false null hypothesis is tested. Which of the following we computed?

(a)beta=P(reject H₀ when H₀ is true)

(b)alpha= P(fail to reject H₀ when H₀ is false)

(c)Power=1-beta

(d)1-alpha