Question

___________I. All daily sales at a convenience store produce a distribution that is approximately normal with a mean of $1220 and a standard deviation of $130. The probability that the sales on a given day at this store are less than $1,305, rounded to four decimal places, is ________?

1. 0.2193           B) 0.7434             C) 0.7993              D) 0.8920

___________II. Let x be a continuous random variable that follows a normal distribution with a mean of 218 and a standard deviation of 26. Find the value of x so that the area under the normal curve to the left of x is approximately 0.8770. Round your answer to two decimal places.

1. 194.18           B) 215.22             C) 248.16             D) 291.80

___________III. The area under the standard normal curve to the right of z is 0.0089. The value of z is ___________?

1. 1.96                B) 2.37                 C) -1.44                D) -2.37

Answer 1

Solution :

1)

Given that ,

mean = = 1220

standard deviation = = 130

P(x < 1305) = P[(x - ) / < (1305 - 1220) / 130]

= P(z < 0.6539)

= 0.7434

2)

P(Z < 1.16) = 0.8770

z = 1.16

Using z-score formula,

x = z * +

x = 1.16 * 26 + 218 = 248.16

3)

P(Z > z) = 0.0089

P(Z < z) = 0.9911

P(Z < -2.37) = 0.9911

z = -2.37