Question

**A random variable is normally distributed with a mean of
80 and a standard deviation of 6.**

**a) Find P(X < 75.5)**

**b) Find P(X > 82)**

**c) Find P(77 < X < 84.8)**

Answer #1

Solution :

Given that ,

mean = = 80

standard deviation = = 6

P(x < 75.5 ) = P[(x - ) / < ( 75.5 - 80) / 6 ]

= P(z < -0.75 )

Using z table,

= 0.2266

**Probability = 0.2266**

( b )

P(x > 82 ) = 1 - P( x < 82 )

= 1- P[(x - ) / < ( 82 - 80) / 6 ]

= 1- P(z < 0.33 )

Using z table,

= 1 - 0.6293

= 0.3707

**Probability = 0.3707**

( c )

P( 77 < x < 84.8 )

= P[( 77 - 80) / 6 ) < (x - ) / < ( 84.8 - 80) / 6 ) ]

= P( -0.5 < z < 0.8 )

= P(z < 0.8 ) - P(z < -0.5 )

Using z table,

= 0.7881 - 0.3085

= 0.4796

**Probability = 0.4796**

assume the random variable X is normally distributed with a mean 80
in standard deviation 9.4
find the P (x>72)
find the P (95<x<105)
find x so that the area above x is .80

assume the random variable x is normally distributed
with mean 80 and standard deviation 4. Find the indicated
Probability P (70<×<76)

Assume that the random variable X is normally distributed, with
mean 80 and standard deviation 15 Compute the probability P(X >
79).

A random variable is normally distributed with a mean of
15 and a standard deviation of 2.5.
Find P(X > 20)
Find P(X < 16.25)
Find P(13.125 < X < 17)

Assume that the random variable X is normally distributed, with
mean μ = 80 and standard deviation σ = 10. Compute the probability
P(95 < X <100).
Answers:
a) 0.1093
b) 0.0823
c) 0.0441
d) 0.0606

Given that a random variable X is normally distributed with a
mean of 80 and a standard deviation of 10, P(85<X,90) is
a.) 0.8413
b.) 0.6915
c.) 0.1498
d.) none of the above

Assume the random variable x is normally distributed with mean
u=90 and standard deviation o=4. Find the indicated probability.
P(77<x<86)

Assume that the random variable X is normally distributed with
mean =50 and standard deviation =18. Find the 11th percentile for
X
A. 27.14
B. 40.28
C. 25.16
D. 27.86

Assume that the random variable X is normally distributed, with
mean =59 and standard deviation of 10 compute the probability
P(56<X ≤ 68)

1.Suppose X is a random variable that is normally distributed with mean 5 and standard deviation 0.4. If P (X≤X0) = P (Z≤1.3). What is the value of X0.?
Select one:
2.00
5.52
6.90
4.48
2.Suppose X is a random variable that is normally distributed with a mean of 5. If P (X≤3) = 0.2005, what is the value of the standard deviation?
Select one:
σ = 2.38
σ = −2
σ = 1.38
σ = 2

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 4 minutes ago

asked 40 minutes ago

asked 45 minutes ago

asked 55 minutes ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago