Question

1) If P(z>k) = 0.9554 then k= ?
2) The mean and standard deviation of the age of bank customers with large checking accounts are 44 and 6, respectively. Then the proportion of such customers that have ages between 35 and 53 is?
3) A Highway Patrol reports the mean speed of those traveling along certen highway is 102 kms per hour with the standard is 7.5 kms per hour. Assume the distribution of speeds follows a normal distribution. 91% of car traveling less than what speed?

Answer 1

1)

P(z>k)=1-P(z<k)

1-P(z<k)=0.9554

P(z<k)=1-0.9554=0.0446

using table z=-1.7

2)

P(35<x<53)=P(x<53)-P(x<35)

P(x<53)

z=$\frac{x-\mu}{\sigma}=\frac{53-44}{6}=1.5$

using table, P(x<53)=0.93319

P(x<35)

z=$\frac{x-\mu}{\sigma}=\frac{35-44}{6}=-1.5$

using table, P(x<35)=0.06681

P(35<x<53)=0.93319-0.06681=0.86638

3)P(x<X)=0.91

using table, z-value=1.34

$\frac{X-102}{7.5}=1.34$

X-102=7.5*1.34=10.05

X=102+10.05=112.05