Question

I am trying to send my question as an attachment

Answer 1

Given:

`\mu=20\text{ ; }\sigma=5`

a)

`P(X\leq25)=P(z\leq(X-\mu)/(\sigma))`
`P(X\leq25)=P(z\leq(25-20)/(5))`
`P(X\leq25)=P(z\leq1)`
`P(X\leq25)=0.8413`
`P(X\leq25)=84.13\text{ \%}`

b)

`P(X\leq35)=P(z\leq(35-20)/(5))`
`P(X\leq25)=P(z\leq3)`
`P(X\leq25)=0.9987`
`P(X\leq25)=99.87\text{ \%}`

c)

`P(X\leq23)=P(z\leq(23-20)/(5))`
`P(X\leq23)=P(z\leq0.6)`
`P(X\leq23)=0.7257`
`P(X\leq23)=72.57\text{ \%}`

d)

`P(X\leq15)=P(z\leq(15-20)/(5))`
`P(X\leq15)=P(z\leq-1)`
`P(X\leq15)=0.1587`
`P(X\leq15)=15.87\text{ \%}`

e)

`P(X\leq17)=P(z\leq(17-20)/(5))`
`P(X\leq17)=P(z\leq-0.6)`
`P(X\leq17)=0.2743`
`P(X\leq17)=27.43\text{ \%}`