Te weight of an adult bottlenose dolphin was found to follow a normal distribution with a mean of 550 pounds and a standard deviation of 50 pounds.
a. what percentage of adult bottlenose dolphins weigh from 400 to 600 pounds?
b. if x represents the mean weight of a random sample of 9 adult bottlenose dolphins, what is p x (500 580 < < ) ?
c. in a random sample of 9 adult bottlenose dolphins, what is the probability that 5 of them are heavier than 560 pounds?

Mean =

Standard deviation =

a. What percentage of adult bottlenose dolphins weigh from 400 to 600 pounds?

P(400<x<600)

Formula :

at x = 400

Refer the z table for p value

p value = 0.0013

at x = 600

Refer the z table for p value

p value = 0.8413

P(400<x<600)=P(x<600)-P(x<400)=0.8413-0.0013=0.84

So,84%  of adult bottlenose dolphins weigh from 400 to 600 pounds

b)If X represents the mean weight of a random sample of 9 adult bottlenose dolphins, what is P (500<x < 580) ?

Formula :

at x = 500

Refer the z table for p value

p value = 0.1587

at x = 580

Refer the z table for p value

p value = 0.7257

P(500<x<580)=P(x<580)-P(x<500)=0.7257-0.1587=0.84

c). In a random sample of 9 adult bottlenose dolphins, what is the probability that 5 of them are heavier than 560 pounds?

at x = 560

Refer the z table for p value

p value = 0.5793

P(x>560)=1-P(x<560)=1-0.5793=0.4207

Now to find the the probability that 5 of them are heavier than 560 pounds we will use binomial distribution

p is the probability of success that is 0.4207

q = 1-p = probability of failure

n = 9

r = 5

Hence In a random sample of 9 adult bottlenose dolphins,  the probability that 5 of them are heavier than 560 pounds is 0.187

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