Question

Mopeds (small motorcycles with an engine capacity below 50 cm3) are very popular in Europe because of their mobility, ease of operation, and low cost. Suppose the maximum speed of a moped is normally distributed with mean value 46.6 km/h and standard deviation 1.75 km/h. Consider randomly selecting a single such moped. (a) What is the probability that maximum speed is at most 49 km/h? (Round your answer to four decimal places.) Incorrect: Your answer is incorrect. (b) What is the probability that maximum speed is at least 47 km/h? (Round your answer to four decimal places.) (c) What is the probability that maximum speed differs from the mean value by at most 2.5 standard deviations? (Round your answer to four decimal places.)

Answer 1

Solution :

Given that ,

mean = = 46.6

standard deviation = = 1.75

a) P(x 49)

= P[(x - ) / (49 - 46.6) / 1.75]

= P(z 1.37)

Using z table,

= 0.9147

b) P(x 47) = 1 - P(x   47 )

= 1 - P[(x - ) / (47 - 46.6) / 1.75 ]

= 1 -  P(z 0.23)   

  Using z table,

= 1 - 0.5910

= 0.4090

c) P( 42.225 < x < 50.975)

= P[(42.225 - 46.6)/1.75 ) < (x - ) /  < (50.975 - 46.6) / 1.75) ]

= P(-2.5 < z < 2.5)

= P(z < 2.5 ) - P(z < -2.5)

Using z table,

= 0.9938 - 0.0062

= 0.9876