Question

4. Leslie has been tasked with putting together a statistical report regarding the use of a particular park in her hometown. Previous data shows that 72% of the residents living in the town visited the park in the last month. She wants to know the probability that more than 98 individuals in a random sample of 150 residents have visited the park in the last month. Please Answer A-C

(a) Based on the information given, is the sample proportion p̂ of residents who have visited the park in the last month approximately normally distributed? Check the appropriate conditions to justify your answer

(b) What is the sample proportion p̂ for Leslies sample of 150 residents? Round your answer to two decimal places?

(c) What is the probability that more than 98 individuals in the random sample of 150 residents have visited the park in the last month?

Answer 1

Solution:

Given that,

n = 150

b ) = 72% =0. 72

1 - = 1 - 0.72 = 0.28

=   = 0. 72

= ( 1 - ) / n

=   0.72 * 0.28 / 150

= 0.0367

= 0.0367

c ) n =150

x =98

= x / n = 98 / 150 = 0.65

P(   > 0.65 )

= 1 - P (   < 0.65 )

= 1 - P ( -    / ) < ( 0.65 - 0.72 / 0.0367 )

= 1 - P ( z < -0.07 / 0.0367 )

= 1 - P ( z < -1.91 )

Using z table

= 1 - 0.0281

= 0.9719

Probability =0.9719