##### Question

In: Statistics and Probability

# Question 1: Assume that the random variable X is normally​ distributed, with mean that = 47...

Question 1: Assume that the random variable X is normally​ distributed, with mean that = 47 and standard deviation that = 7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded.

P(X< AND = TO 43)

Using technology, what is P(X< AND = TO 43) equal? (round to four decimal places)

• How did you find this answer using a graphing calculator??

Question 2: The mean incubation time for a type of fertilized egg kept at 100.8​°F is 22 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 2 days.

(a) What is the probability that a randomly selected fertilized egg hatches in less than 20 ​days?

​(b) What is the probability that a randomly selected fertilized egg takes over 24 days to​ hatch?

​(c) What is the probability that a randomly selected fertilized egg hatches between 18 and 22 ​days?

​(d) Would it be unusual for an egg to hatch in less than 17 ​days? Why?

• How did you find these answers? Thanks!

## Solutions

##### Expert Solution

Since the random variable X is normally distributed, with mean that = 47 and standard deviation that = 7 hence

to find

a) is calculated using the Z score calculator as

hence

P(X</=43)=P(Z</=-0.57)

The probability value is calculated using the Z table shown below as

P-value=0.2843

b) since the mean incubation time for a type of fertilized egg kept at 100.8 °F is 22 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 2 days.

hence,

a) P(X<20)

Using Z formula

P(Z<-1)=0.1587 using Z table

b) P(X.>24)

P(Z>1)=0.1587 again computed using the Z table shown below

c) P(18<X<22)

Z at X=18

and Z at X=22

So, P(10<X<22)

=P(-2<Z<0)

=0.50-0.0228

=0.4772

d) Again P(X<17)

According to Central limit theorem if Z value is less than -2 and greater than 2 then by rare event rule the probability of happening that event becomes very low hence it is unusual.

Z table

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