Question

A. Let x be a continuous random variable that is normally distributed with mean μ=24 and standard deviation σ=4. Use a graphing calculator to find P(20≤x≤33). The probability is? (Round to 4 decimal places)

B. Let x be a continuous random variable that is normally distributed with mean μ=27 and standard deviation σ=4. Use a graphing calculator to find P(19≤x≤35). The probability is? (Round to 4 decimal places)

C. Let x be a continuous random variable that is normally distributed with mean μ=21 and standard deviation σ=2. Use a graphing calculator to find P(16≤x≤24). The probability is? (Round to 4 decimal places)

Answer 1

Solution :

a ) Given that,

mean = = 24

standard deviation = = 4

P( 20 x 33 )

P ( 20 - 24 / 4) < ( x -  / ) < ( 33 - 24 / 4)

P ( - 4 / 4 z 13 /4 )

P (-1 z 3.25)

P ( z < 3.25 ) - P ( z < -1)

Using z table

= 0.9994 - 0.1587

= 0.8407

Probability = 0.8407

b ) Given that,

mean = = 27

standard deviation = = 4

P( 19 x 33 )

P ( 19 - 27 / 4) < ( x -  / ) < ( 35 - 27 / 4)

P ( - 8 / 4 z 8 /4 )

P (-2 z 2)

P ( z < 2 ) - P ( z < 2)

Using z table

= 0.9772 - 0.0228

= 0.9544

Probability = 0.9544

c ) Given that,

mean = = 21

standard deviation = = 2

P( 16 x 33 )

P ( 16 - 21 /2) < ( x -  / ) < ( 24- 21 / 2)

P ( - 5 / 2 z 3 /2 )

P (-2.5 z 1.5)

P ( z < 1.5 ) - P ( z < -2.5)

Using z table

= 0.9332 - 0.0062

= 0.9270

Probability = 0.9270