Question

(1 point) Length of skateboards in a skateshop are normally distributed with a mean of 31.9 in and a standard deviation of 0.4 in. The figure below shows the distribution of the length of skateboards in a skateshop. Calculate the shaded area under the curve. Express your answer in decimal form with three decimal place accuracy. Answer: 31.632 32.7 The Length of Skateboards in a Skateshop

Answer 1

Solution :

Given that ,

mean = $\mu$ = 31.9

standard deviation = $\sigma$ = 0.4

P(31.632< x <32.7 ) = P[(31.632 -31.9) /0.4 < (x - $\mu$ ) / $\sigma$ < (32.7 -31.9) /0.4 )]

= P( -0.67< Z <2 )

= P(Z <2 ) - P(Z <-0.67 )

Using z table   

= 0.9772 -0.2514

   probability= 0.7258