The amount of carbon monoxide exposure of someone riding a motorbike for 5 km on

Question

The amount of carbon monoxide exposure of someone riding a motorbike for 5 km on a highway in Hanoi is approximately normally distributed with a mean of 18.6 ppm and a standard deviation of 5.7 ppm.

a.) State the random variable.

b.) Find the probability that a rider of a motorbike for 5 km on a Hanoi highway will experience a carbon monoxide exposure of more than 20 ppm.

c.) Find the probability that a rider of a motorbike for 5 km on a Hanoi highway will experience a carbon monoxide exposure of less than 25 ppm.

d.) Find the probability that a rider of a motorbike for 5 km on a Hanoi highway will experience a carbon monoxide exposure of between 10 and 24 ppm.

Explanation / Answer

Here, n = 5 , mean = 18.6 , sd = 5.7

b) x =20

By normal distribution formula,

z = (x - mean) / (sd/ sqrt(n))

= (20 - 18.6 ) / ( 5.7 / sqrt(5))

= 0.54

Now, we neeed to find P(z >0.54)

p(x >20) = p(z > 0.54) = .2908

c)

Here, n = 5 , mean = 18.6 , sd = 5.7

x =25

By normal distribution formula,

z = (x - mean) / (sd/ sqrt(n))

= (25 - 18.6 ) / ( 5.7 / sqrt(5))

= 2.51

Now, we neeed to find P(z <2.51)

p(x <25) = p(z < 2.51) = .9941

d)

Here, n = 5 , mean = 18.6 , sd = 5.7

x1 = 10, x2 = 24

By normal distribution formula,

z = (x - mean) / (sd/ sqrt(n))

= ((10 - 18.6 ) / ( 5.7 / sqrt(5) < z < (24 - 18.6 ) / ( 5.7 / sqrt(5) )

= (-3.37 < z < 2.11)

Now, we neeed to find P( -3.37 < z < 2.11)

p( 10 < x < 24) = p( -3.37 < z < 2.11) = .9829

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.