Question

6.The lengths of a population of certain HULU movies I watch are normally distributed with a mean running time of 110 minutes and a standard deviation of 17.5.

Since this population is normally distributed it will be skewed to the right.

True or False

7. The z-score associated with a movie that has a running time of 110 minutes is 0. True or False

8. The z-score associated with a movie that has a running time of 108.5 minutes is 0.09

9.We can find 34% of the data between 92.5 and 110 minutes.

True or false

Answer 1

Solution :

Given that ,

mean = $\mu$ = 110

standard deviation = $\sigma$ = 17.5

6) false, mean, median, and mode always equal in normal distribution

7) x = 110

Using z-score formula,

z = x - $\mu$ / $\sigma$   

z = 110 - 110 / 17.5

z = 0

True

8) x = 108.5

Using z-score formula,

z = x - $\mu$ / $\sigma$   

z = 108.5 - 110 / 17.5

z = -0.09

False

9) P( 92.5 < x < 110 ) = P[(92.5 - 110 ) / 17.5) < (x - $\mu$ ) /$\sigma$  < (110 - 110 ) / 17.5) ]

= P( -1.00 < z < 0)

= P(z < 0) - P(z < -1.00)

Using z table,

= 0.5 - 0.16

= 0.34

The percentage is = 34%

True