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SCORPION-xisa [38]
3 years ago
13

A certain tennis player makes a successful first serve 6969​% of the time. Suppose the tennis player serves 9090 times in a matc

h. ​a)​ What's the mean and standard deviation of the number of good first serves​ expected? ​b) Determine if you can use a normal model to approximate the distribution of the number of good first serves. ​c)​ What's the probability she makes at least 7272 first​ serves?
Mathematics
1 answer:
Wewaii [24]3 years ago
8 0

Answer:

a) 4.387

b) Yes, because np & npq are greater than 10.

c) = 0.017          

Step-by-step explanation:

Give data:

p = 0.69

n = 90

a) a

E(X) = np = 62.1

SD(X) = \sqrt{(np(1-p))}

          =\sqrt{90\times 0.69(1- 0.69)}

          = 4.387

b)

np = 62.1  

q = 1 - p  = 1 - 0.69 = 0.31

npq = 19.251

Yes, because np & npq are greater than 10.

c.

P(X \geq 72   ) = P(X > 71.5) [continuity correction]

=    P(Z> \frac{((71.5-62.1)}{ 4.387})

= P(Z> 2.14 )      

= 1 - P(Z<2.14)              

= 1 - 0.983   (using table)          

= 0.017          

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