Question

Draw a picture of the standard normal curve and shade the area that corresponds to the requested probabilities. Then use the standard normal table to find the following probabilities. Enter the probabilities as decimals. Enter the final answer only. 1.P(z>1.38)= 2.P(1.233 −2.43)= 7.P(z>−2.43)=

Answer 1

a)P [ z > 1,38 ] = 0,08379

b) P [ 1,233 < z < 2,43 ] = 0,1012

c) P [ z > -2,43 ] = 0,99245

Explanation:

a) P [ z > 1,38 ] = 1 - P [ z < 1,38 ]

From z-table P [ z < 1,38 ] = 0,91621

P [ z > 1,38 ] = 1 - 0,91621

P [ z > 1,38 ] = 0,08379

b) P [ 1,233 - 2,43 ] must be P [ 1,233 < z < 2,43 ]

P [ 1,233 < z < 2,43 ] = P [ z < 2,43 ] - P [ z > 1,233 ]

P [ z < 2,43 ] = 0,99245

P [ z > 1,233 ] = 0,89125 ( approximated value without interpolation)

Then

P [ 1,233 < z < 2,43 ] = 0,99245 - 0,89125

P [ 1,233 < z < 2,43 ] = 0,1012

c) P [ z > -2,43 ]

Fom z-table

P [ z > -2,43 ] = 1 - P [ z < -2,43 ]

P [ z > -2,43 ] = 1 - 0,00755

P [ z > -2,43 ] = 0,99245