Question

Question 5 

Measurements were recorded for the slapshot speed of 100 minor-league hockey players. These measurements were found to be normally distributed with mean of 88.421 mph and standard deviation of 3.5543 mph. Would it be unusual to record a value below 80.55 mph?

Question 5 options:

	1) The value is borderline unusual.
	2) The value is unusual.
	3) It is impossible for this value to occur with this distribution of data.
	4) We do not have enough information to determine if the value is unusual.
	5) The value is not unusual.

Question 6 

Pinterest claims that 0.3719 of their app users are men. In a sample of 78 randomly chosen app users, what is the probability that less than 36 of them will be men?

Question 6 options:

	1) 0.9590
	2) 0.9345
	3) 0.0245
	4) 0.0655
	5) 0.0122

Question 7 

Pinterest claims that 0.3808 of their app users are men. In a sample of 74 randomly chosen app users, what is the probability that between 29 and 31 (inclusively) of them will be men?

Question 7 options:

	1) 1.4148
	2) 0.7467
	3) 0.2533
	4) -0.0204
	5) 0.1676

Question 8 

Pinterest claims that 0.3249 of their app users are men. In a sample of 61 randomly chosen app users, what is the probability that no more than 25 of them will be men?

Question 8 options:

	1) 0.9376
	2) 0.0394
	3) 0.8982
	4) 0.0197
	5) 0.0624

Question 9

According to a survey conducted by Deloitte in 2017, 0.46 of U.S. smartphone owners have made an effort to limit their phone use in the past. In a sample of 80 randomly selected U.S. smartphone owners, approximately __________ owners, give or take __________, will have attempted to limit their cell phone use in the past. Assume each pick is independent.

Question 9 options:

	1) 80 , 4.458
	2) 4.458 , 36.8
	3) 36.8 , 4.458
	4) 36.8 , 0.46
	5) 36.8 , 19.90

Answer 1

5)

µ =    88.421      
σ =    3.5543      
          
P( X ≤    80.55   ) = P( (X-µ)/σ ≤ (80.55-88.421) /3.5543)  
=P(Z ≤   -2.21   )

values which are  2 std dev away from mean are unusual to occur

so,answer is The value is unusual.

6)

n=78

p=0.3719

Binomial probability is given by

P(X=x) = C(n,x)*px*(1-p)(n-x)

P(x<36) = Σ C(n,x)*p^x*(1-p)^(n-x)= 0.9345

7)

Sample size , n =    74
Probability of an event of interest, p =   0.3808
P ( X = 29) = C (74,29) * 0.3808^29 * ( 1 - 0.3808)^45=      0.0929
P ( X = 30) = C (74,30) * 0.3808^30 * ( 1 - 0.3808)^44=   0.0857
P ( X = 31) = C (74,31) * 0.3808^31 * ( 1 - 0.3808)^43=   0.0748

P(29≤x≤31) = 0.2533

8)

Sample size , n =    61
Probability of an event of interest, p =   0.3249

P(x≤25) = Σ C(n,x)*p^x*(1-p)^(n-x)= 0.9376

9)

Sample size , n =    80
Probability of an event of interest, p =   0.46

Mean = np =    80   *   0.460   =           36.80

Standard deviation = √(np(1-p)) =   √   19.8720   =               4.458

answer is :

36.8 , 4.458