Mathematics: The distribution of passenger vehicle speeds traveling on a certain freeway in california is nearly normal with a mean of 73.7 miles/hour and a standard deviation of 4.77 miles/hour. (a) what percent of passenger vehicles travel slower than 80 miles/hour? (round your answer to two decimal places.) % (b) what percent of passenger vehicles travel between 60 and 80 miles/hour? (round your answer to two decimal places.) % (c) how fast do the fastest 5% of passenger vehicles travel? (round your answer

The distribution of passenger vehicle speeds traveling

sonnyboi2305

06.01.2022

A) 90.32%

B) 90.11%

C) 81.546 miles per hour

D)77.93%

Step-by-step explanation:

Given data:

speed = 73.7 miles/hour

standard deviation = 4.77 miles /hour

a) $P(X< 80) = P(z< \frac{80 - 73.7}{4.77}$

= P (z< 1.31)

= 0.90320 = 90.32%

b) $P(60 < X< 80) = P(\frac{60 - 73.7}{4.77} < z< \frac{80 - 73.7}{4.77})$

= P (-2.872< z< 1.31)

= P (z<1.31) - P(z<-2.87)

= 0.90320 - 0.00205

= 0.90115 = 90.11%

c) P(X <X) = 0.95

z = 1.645

$\frac{x - 73.7}{4.77} = 1.645$

x = 81.546 miles per hour

$d)P(X< 70) = P(z \frac{70 - 73.7}{4.77})$

= P (z> -0.775)

= 0. 0.7793 = 77.93%

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