Question

9. Women have pulse rates that are normally distributed with a mean of 73.3 beats per minute and a standard deviation of 11.3 beats per minute. Complete parts a through c below.

a. Find the percentiles 1P1 and P99.

P1=_____ beats per minute

​(Round to one decimal place as​ needed.)

10. An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150 lb and 191 lb. The new population of pilots has normally distributed weights with a mean of 156 lb and a standard deviation of 26.9 lb.

a. If a pilot is randomly​ selected, find the probability that his weight is between 150 lb and 191 lb.

The probability is approximately_____

​(Round to four decimal places as​ needed.)

Answer 1

9. We have,

and  

1^st percentiles i.e P1 is given by :

P(Z < z*) = 0.01, from standard normal table z* = -2.326

99percentiles i.e P99 is given by :

P(Z < z*) = 0.99, from standard normal table z* = 2.326

  

10.   = 156 lb, = 26.9 lb

We want to find P(150 lb < x < 191 lb)

= P((150 - 156)/26.9< Z < 191 - 156)/26.9)

= P (0.2230 < Z <1.3011)

= P(Z<1.3011 ) − P(Z<0.2230 )

= 0.9032 - 0.5871

= 0.3161