Is Lacking of sleep causing traffic fatalities A study cond

Is Lacking of sleep causing traffic fatalities. ? A study conducted under the auspices of the Nation Highway Traffic Safety administration found that the average number of fatal cadres caused by drow drivers each year was 1550. Assume that the annual number of fatal crashes per year is norma distributed with a standard deviation or 300. What is the probability of at least 1000 fatal eras per year between 700 and 800 Find p (-infinity

Solution

a) let X = annual no. of fata crasesh per year

P [ X >= 1000] = P [ ( X-mean) / s.d >= ( 1000 - 1550) / 300 ] = p [ z >= -1.833333]

= 1 - p [ z < -1.833333] = 0.9666235.....

P [ 700 < X < 800 ] =P [ (700-1550) / 300 < Z < ( 800-1550)/300 ] = P [ Z < -2.5] - P[ Z <  -2.833333]

= 0.003906397.......

Q2) P [ -infinity < Z < + infinity ] = 1...[ as -infinity to +infinity is whole range of normal distribution and max area=1]

P [ Z < 1.25 ] = 0.8943502...