What is the probability that the mean vertical leap for the 36 players will be b

Question

What is the probability that the mean vertical leap for the 36 players will be between 27.5 and 28.5 inches? A high-priced athletic trainer has been hired to work with a group of NBA players to improve their hip flexibility which should improve their vertical leap. After one month of training the mean vertical leap for 50 of these player's evidence to suggest this flexibility program has increased the mean vertical leap (from mu = 28 inches)? The ozone hole is a region in the southern Hemisphere that has increased since 1979. The mean ozone hole area (in million km^2) in 2012 was 17.9^16 with standard deviation 5.6. Suppose 33 days are selected at random and the ozone hole is measured each day. What is the probability that the sample mean ozone hole area is less than 15.5 million km^2? What is the probability that the sample mean ozone hole area is between 16 and 18 million km^2? Some researchers suggest that increased use so chemicals has caused the ozone hole area to increas

Explanation / Answer

as we know that z=(X-mean)/std deviation

a)hence P(X<15.5)=P(Z<(15.5-17.9)/5.6)=P(Z<-0.4286)=0.3341

b)P(16<X<18)=P(-0.3393<Z<0.0179)=0.5071-0.3672=0.1399

c)for 33 days std error of mean =std deviation/(n)1/2 =0.9748

hence test stat z=(X-mean)/std error =(20.7-17.9)/0.9748 =2.8723

for above test stat p value =0.002

as p value is significantly low there is sufficient evidence to suggest that mean ozone hole area has been increased

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